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DP IB Physics: HL

Revision Notes

Home / IB / Physics: HL / DP / Revision Notes / 10. Fields (HL only) / 10.1 Describing Fields / 10.1.3 Gravitational & Electrostatic Potential


10.1.3 Gravitational & Electrostatic Potential


Gravitational & Electrostatic Potential

Gravitational Potential

  • The gravitational potential energy (G.P.E) is the energy an object has when lifted off the ground
  • G.P.E is given by the familiar equation:
GPE = mgh

  • The G.P.E on the surface of the Earth is taken to be zero
    • This means work is done to lift the object
    • The equation is only valid for objects that are close to the Earth's surface
  • However, outside the Earth’s immediate influence, G.P.E can be better defined as:

The energy an object possess due to its position in a gravitational field

  • The gravitational potential at a point can, therefore, be defined as:

The work done per unit mass in bringing a test mass from infinity to a defined point

  • It is represented by the symbol, V and is measured in J kg−1
  • Gravitational potential is always a negative value, this is because:
    • It is defined as having a value of zero at infinity
    • Since the gravitational force is attractive, work must be done on a mass to reach infinity
  • On the surface of a mass (such as a planet), gravitational potential has a negative value
    • The value becomes less negative, i.e. it increases, with distance from that mass
  • Work has to be done against the gravitational pull of the planet to take a unit mass away from the planet
  • The gravitational potential at a point depends on:
    • The mass of the object producing the gravitational field
    • The distance the centre of mass to the point

Gravitational Potential

Gravitational potential decreases as the satellite moves closer to the Earth

Gravitational Potential Difference

  • Two points at different distances from a mass will have different gravitational potentials because the gravitational potential increases with distance
  • So there will also be a gravitational potential difference between the two points, which is represented by the symbol ΔV
  • Gravitational potential difference, ΔV, is given by:
capital delta V equals V subscript f minus V subscript i
  • Where:
    • Vf = final gravitational potential (J kg−1)
    • Vi = initial gravitational potential (J kg−1)
  • A difference in gravitational potential will give a difference in gravitational potential energy, which can also be calculated

Calculating Gravitational Potential

  • The equation for gravitational potential V is defined by the mass M and distance r:
V equals negative fraction numerator G cross times M over denominator r end fraction

  • Where:
    • V = gravitational potential (J kg-1)
    • G = Newton’s gravitational constant
    • M = mass of the body producing the gravitational field (kg)
    • r = distance from the centre of the mass to the point mass (m)

  • The gravitational potential always is negative near an isolated mass, such as a planet, because:
    • The potential when r is at infinity (∞) is defined as 0
    • Work must be done to move a mass away from a planet (V becomes less negative)

  • It is also a scalar quantity, unlike the gravitational field strength which is a vector quantity

  • Gravitational forces are always attractive, this means as r decreases, positive work is done by the mass when moving from infinity to that point
    • When a mass is closer to a planet, its gravitational potential becomes smaller (more negative)
    • As a mass moves away from a planet, its gravitational potential becomes larger (less negative) until it reaches 0 at infinity

  • This means when the distance (r) becomes very large, the gravitational force tends rapidly towards 0 at a point further away from a planet

13.2.1.2 Gravitational potential diagram_1

Gravitational potential increases and decreases depending on whether the object is travelling towards or against the field lines from infinity

Worked Example

A planet has a diameter of 7600 km and a mass of 3.5 × 1023 kg. A rock of mass 528 kg accelerates towards the planet from infinity.

Calculate the gravitational potential of the rock at a distance of 400 km above the planet's surface.

Step 1: Write the gravitational potential equation

V equals negative fraction numerator G cross times M over denominator r end fraction
Step 2: Determine the value of r

    • r is the distance from the centre of the planet
Radius of the planet = planet diameter ÷ 2 = 7600 ÷ 2  = 3800 km
r = 3800 + 400 = 4200 km = 4.2 × 106 m

Step 3: Substitute in values

V equals negative fraction numerator left parenthesis 6.67 cross times 10 to the power of negative 11 end exponent right parenthesis cross times left parenthesis 3.5 cross times 10 to the power of 23 right parenthesis over denominator 4.2 cross times 10 to the power of 6 end fraction equals negative 5.6 cross times 10 to the power of 6 space J space k g to the power of negative 1 end exponent

Graphical Representation of Gravitational Potential

  • Gravitational field strength, g and the gravitational potential, V can be graphically represented against the distance from the centre of a planet, r

  • g, V and r are related by the equation:
g equals negative fraction numerator capital delta V over denominator capital delta r end fraction
  • Where:
    • g = gravitational field strength (N kg-1)
    • ΔV = change in gravitational potential (J kg-1)
    • Δr = distance from the centre of a point mass (m)

  • The graph of V against r for a planet is:


Gravitational Potential and Distance Graph, downloadable AS & A Level Physics revision notes

The gravitational potential and distance graphs follows a -1/r relation
  • The key features of this graph are:
    • The values for V are all negative
    • As r increases, V against r follows a -1/r relation
    • The gradient of the graph at any particular point is the value of g at that point
    • The graph has a shallow increase as r increases

  • To calculate g, draw a tangent to the graph at that point and calculate the gradient of the tangent
    • This gives you a graphical representation of the equation:
V equals negative fraction numerator G M over denominator r end fraction

  • Where G and M are constant
  • The graph of g against r for a planet is:


Gravitational Field Strength and Distance Graph, downloadable AS & A Level Physics revision notes

The gravitational field strength and distance graph follows a 1/r2 relation
  • The key features of this graph are:
    • The values for g are all positive
    • As r increases, g against r follows a 1/r2 relation (inverse square law)
    • The area under this graph is the change in gravitational potential ΔV
    • The graph has a steep decline as r increases

  • The area under the graph can be estimated by counting squares, if it is plotted on squared paper, or by splitting it into trapeziums and summing the area of each trapezium
    • The inverse square law relation means that as the distance r doubles, the value of g decreases by a factor of four
  • This is a graphical representation of the equation:

g equals fraction numerator G M over denominator r squared end fraction
  • Where G and M are constant

Worked Example

Sketch a graph on the axes below to indicate how the gravitational potential varies with distance along a line outwards from the surface of planet A which is 80 times the mass of planet B.

Worked Example V against r Graph Question, downloadable AS & A Level Physics revision notes

Worked Example V against r Graph Solution, downloadable AS & A Level Physics revision notes

  • Graph increases from a large negative value for V at the surface of A as distance increases
  • Up to a value close to, but below 0 near the surface of planet B
  • The graph then falls near the surface of planet B
  • From a point much closer to planet B than A

Electric Potential

  • In order to move a positive charge closer to another positive charge, work must be done to overcome the force of repulsion between them
    • Similarly, to move a positive charge away from a negative charge, work must be done to overcome the force of attraction between them

  • Energy is therefore transferred to the charge that is being pushed upon
    • This means its potential energy increases

  • If the positive charge is free to move, it will start to move away from the repelling charge
    • As a result, its potential energy decreases back to 0

  • This is analogous to the gravitational potential energy of a mass increasing as it is being lifted upwards and decreasing as it falls
  • The electric potential at a point is defined as:

The work done per unit positive charge in bringing a point test charge from infinity to a defined point

  • Electric potential is a scalar quantity
    • This means it doesn’t have a direction

  • However, electric potential can have a positive or negative sign, this is because it is:
    • Positive around an isolated positive charge
    • Negative around an isolated negative charge
    • Zero at infinity

  • Positive work is done by the mass from infinity to a point around a positive charge and negative work is done around a negative charge. This means:
    • When a positive test charge moves closer to a negative charge, its electric potential decreases
    • When a positive test charge moves closer to a positive charge, its electric potential increases

  • To find the potential at a point caused by multiple charges, the total potential is the sum of the potential from each charge

Electric Potential around Positive & Negative Charges 1, downloadable AS & A Level Physics revision notes
Electric Potential around Positive & Negative Charges 2, downloadable AS & A Level Physics revision notes

The electric potential V decreases in the direction the test charge would naturally move in due to repulsion or attraction

Electric Potential Difference

  • Two points at different distances from a charge will have different electric potentials
    • This is because the electric potential increases with distance from a negative charge and decreases with distance from a positive charge

  • Therefore, there will be an electric potential difference between the two points
    • This is represented by the symbol ΔV

  • ΔV is normally given as the equation
capital delta V equals V subscript f minus V subscript i

  • Where:
    • Vf = final electric potential (J C-1)
    • Vi = initial electric potential (J C-1)

  • A difference in electric potential will give a difference in electric potential energy, which can also be calculated

Graphical Representation of Electric Potential

  • Electric field strength, E and the electric potential, V can be graphically represented against the distance from the centre of a charge, r

  • E, V and r are related by the equation:
E equals fraction numerator capital delta V over denominator capital delta r end fraction
  • Where:
    • E = electric field strength (V m-1)
    • ΔV = change in potential (V)
    • Δr = displacement in the direction of the field (m)
  • An electric field can be defined in terms of the variation of electric potential at different points in the field:

The electric field at a particular point is equal to the gradient of a potential-distance graph at that point

  • The potential gradient in an electric field is defined as:

The rate of change of electric potential with respect to displacement in the direction of the field

  • The graph of potential V against distance r for a negative or positive charge is:

Electric Potential Gradient Graph, downloadable AS & A Level Physics revision notes

The electric potential around a positive charge decreases with distance and increases with distance around a negative charge

  • The key features of this graph are:
    • The values for V are all negative for a negative charge
    • The values for V are all positive for a positive charge
    • As r increases, V against r follows a 1/r relation for a positive charge and -1/r relation for a negative charge
    • The gradient of the graph at any particular point is the value of E at that point
    • The graph has a shallow increase (or decrease) as r increases

  • The electric potential changes according to the charge creating the potential as the distance r increases from the centre:
    • If the charge is positive, the potential decreases with distance
    • If the charge is negative, the potential increases with distance

  • To calculate E, draw a tangent to the graph at that point and calculate the gradient of the tangent
  • This is a graphical representation of the equation:
V equals fraction numerator Q over denominator 4 pi epsilon subscript o r end fraction
  • Where Q and 4πε0 are constants
  • The graph of E against r for a charge is:

Electric Field Strength and Distance Graph, downloadable AS & A Level Physics revision notes

The electric field strength E has a 1/r2 relationship

  • The key features of this graph are:
    • The values for E are all positive
    • As r increases, E against r follows a 1/r2 relation (inverse square law)
    • The area under this graph is the change in electric potential ΔV
    • The graph has a steep decline as r increases

  • The area under the graph can be estimated by counting squares, if it is plotted on squared paper, or by splitting it into trapeziums and summing the area of each trapezium
  • The inverse square law relation means that as the distance r doubles, E decreases by a factor of 4

  • This is a graphical representation of the equation:
E equals fraction numerator Q over denominator 4 pi epsilon subscript o r squared end fraction
  • Where Q and 4πε0 are constants

Exam Tip

Drawing, interpreting or calculating from inverse square law graphs are common exam questions - there are lots of similarities between gravitational and electric field graphs:

Graphs of field strength against distance should start off steeper and decrease rapidly compared to that of potential graphs against distance, to distinguish it as an inverse square law (1/r2) relation instead of just an inverse relation (1/r)

There are plenty of differences too:

For example, gravitational potential always increases with respect to distance whereas electric potential can increase or decrease

One way to remember whether the electric potential increases or decreases with respect to the distance from the charge is by the direction of the electric field lines - the potential always decreases in the same direction as the field lines and vice versa.



  • 1. Measurement & Uncertainties
    • 1.1 Measurements in Physics
      • 1.1.1 SI Units
        • 1.1.2 Using Scientific Notation
          • 1.1.3 Estimating Physical Quantities
          • 1.2 Uncertainties & Errors
            • 1.2.1 Random & Systematic Errors
              • 1.2.2 Calculating Uncertainties
                • 1.2.3 Determining Uncertainties from Graphs
                • 1.3 Vectors & Scalars
                  • 1.3.1 Vector & Scalar Quantities
                    • 1.3.2 Combining & Resolving Vectors
                      • 1.3.3 Solving Vector Problems
                    • 2. Mechanics
                      • 2.1 Motion
                        • 2.1.1 Distance & Displacement
                          • 2.1.2 Speed & Velocity
                            • 2.1.3 Acceleration
                              • 2.1.4 Graphs Describing Motion
                                • 2.1.5 Uniform Acceleration
                                  • 2.1.6 Acceleration of Free Fall Experiment
                                    • 2.1.7 Projectile Motion
                                      • 2.1.8 Terminal Speed
                                      • 2.2 Forces
                                        • 2.2.1 Free-Body Diagrams
                                          • 2.2.2 Newton’s First Law
                                            • 2.2.3 Newton’s Second Law
                                              • 2.2.4 Newton’s Third Law
                                                • 2.2.5 Applying Newton’s Laws of Motion
                                                  • 2.2.6 Friction
                                                  • 2.3 Work, Energy & Power
                                                    • 2.3.1 Kinetic Energy
                                                      • 2.3.2 Gravitational Potential Energy
                                                        • 2.3.3 Elastic Potential Energy
                                                          • 2.3.4 Work Done
                                                            • 2.3.5 Power
                                                              • 2.3.6 Principle of Conservation of Energy
                                                                • 2.3.7 Efficiency
                                                                • 2.4 Momentum & Impulse
                                                                  • 2.4.1 Force & Momentum
                                                                    • 2.4.2 Impulse
                                                                      • 2.4.3 Conservation of Linear Momentum
                                                                        • 2.4.4 Collisions & Explosions
                                                                      • 3. Thermal Physics
                                                                        • 3.1 Thermal Concepts
                                                                          • 3.1.1 Solids, Liquids & Gases
                                                                            • 3.1.2 Temperature
                                                                              • 3.1.3 Internal Energy
                                                                                • 3.1.4 Specific Heat Capacity
                                                                                  • 3.1.5 Specific Latent Heat
                                                                                    • 3.1.6 Phase Change
                                                                                      • 3.1.7 Investigating Thermal Energy
                                                                                      • 3.2 Modelling a Gas
                                                                                        • 3.2.1 Ideal Gas Laws
                                                                                          • 3.2.2 Ideal Gas Equation
                                                                                            • 3.2.3 Kinetic Model of an Ideal Gas
                                                                                              • 3.2.4 Mole Calculations
                                                                                                • 3.2.5 Investigating Gas Laws
                                                                                              • 4. Waves
                                                                                                • 4.1 Oscillations
                                                                                                  • 4.1.1 Properties of Oscillations
                                                                                                    • 4.1.2 Simple Harmonic Oscillations
                                                                                                      • 4.1.3 SHM Graphs
                                                                                                        • 4.1.4 Energy in SHM
                                                                                                        • 4.2 Travelling Waves
                                                                                                          • 4.2.1 Properties of Waves
                                                                                                            • 4.2.2 Transverse & Longitudinal Waves
                                                                                                              • 4.2.3 Electromagnetic Waves
                                                                                                                • 4.2.4 Sound Waves
                                                                                                                • 4.3 Wave Characteristics
                                                                                                                  • 4.3.1 Wavefronts
                                                                                                                    • 4.3.2 Amplitude & Intensity
                                                                                                                      • 4.3.3 Superposition
                                                                                                                        • 4.3.4 Polarisation
                                                                                                                          • 4.3.5 Malus’s Law
                                                                                                                          • 4.4 Wave Behaviour
                                                                                                                            • 4.4.1 Reflection, Refraction & Transmission
                                                                                                                              • 4.4.2 Reflection
                                                                                                                                • 4.4.3 Refraction
                                                                                                                                  • 4.4.4 Determining Refractive Index
                                                                                                                                    • 4.4.5 Single-Slit Diffraction
                                                                                                                                      • 4.4.6 Interference & Path Difference
                                                                                                                                        • 4.4.7 Double-Slit Equation
                                                                                                                                        • 4.5 Standing Waves
                                                                                                                                          • 4.5.1 The Nature of Standing Waves
                                                                                                                                            • 4.5.2 Nodes & Antinodes
                                                                                                                                              • 4.5.3 Boundary Conditions for Standing Waves
                                                                                                                                                • 4.5.4 Harmonics
                                                                                                                                              • 5. Electricity & Magnetism
                                                                                                                                                • 5.1 Electric Fields
                                                                                                                                                  • 5.1.1 Charge & Current
                                                                                                                                                    • 5.1.2 Drift Speed
                                                                                                                                                      • 5.1.3 Potential Difference & DC
                                                                                                                                                        • 5.1.4 Electric Fields
                                                                                                                                                          • 5.1.5 Coulomb’s Law
                                                                                                                                                          • 5.2 Heating Effect of Electric Currents
                                                                                                                                                            • 5.2.1 Circuits
                                                                                                                                                              • 5.2.2 Resistance & Resistors
                                                                                                                                                                • 5.2.3 Kirchhoff’s Circuit Laws
                                                                                                                                                                  • 5.2.4 I-V Characteristics
                                                                                                                                                                    • 5.2.5 Resistivity
                                                                                                                                                                      • 5.2.6 Investigating Resistivity
                                                                                                                                                                        • 5.2.7 Series & Parallel Circuits
                                                                                                                                                                          • 5.2.8 Heating Effect of Current
                                                                                                                                                                            • 5.2.9 Potential Divider Circuits
                                                                                                                                                                            • 5.3 Electric Cells
                                                                                                                                                                              • 5.3.1 Primary & Secondary Cells
                                                                                                                                                                                • 5.3.2 Investigating Electric Cells
                                                                                                                                                                                  • 5.3.3 Terminal Potential Difference
                                                                                                                                                                                    • 5.3.4 Electromotive Force & Internal Resistance
                                                                                                                                                                                    • 5.4 Magnetic Effects of Electric Currents
                                                                                                                                                                                      • 5.4.1 Magnetic Fields
                                                                                                                                                                                        • 5.4.2 Magnetic Force on a Charge
                                                                                                                                                                                          • 5.4.3 Magnetic Force on a Current-Carrying Conductor
                                                                                                                                                                                            • 5.4.4 Solving Problems Involving Magnetic Forces
                                                                                                                                                                                          • 6. Circular Motion & Gravitation
                                                                                                                                                                                            • 6.1 Circular Motion
                                                                                                                                                                                              • 6.1.1 Circular Motion
                                                                                                                                                                                                • 6.1.2 Centripetal Force
                                                                                                                                                                                                  • 6.1.3 Centripetal Acceleration
                                                                                                                                                                                                    • 6.1.4 Applications of Circular Motion
                                                                                                                                                                                                    • 6.2 Newton’s Law of Gravitation
                                                                                                                                                                                                      • 6.2.1 Newton’s Law of Gravitation
                                                                                                                                                                                                        • 6.2.2 Circular Orbits
                                                                                                                                                                                                          • 6.2.3 Gravitational Field Strength
                                                                                                                                                                                                        • 7. Atomic, Nuclear & Particle Physics
                                                                                                                                                                                                          • 7.1 Discrete Energy & Radioactivity
                                                                                                                                                                                                            • 7.1.1 Discrete Energy Levels
                                                                                                                                                                                                              • 7.1.2 Calculating Discrete Energies
                                                                                                                                                                                                                • 7.1.3 Emission & Absorption Spectrum
                                                                                                                                                                                                                  • 7.1.4 Isotopes & Radioactive Decay
                                                                                                                                                                                                                    • 7.1.5 Background Radiation
                                                                                                                                                                                                                      • 7.1.6 Alpha, Beta & Gamma Particles
                                                                                                                                                                                                                        • 7.1.7 Decay Equations
                                                                                                                                                                                                                          • 7.1.8 Half-Life
                                                                                                                                                                                                                            • 7.1.9 Investigating Half-Life
                                                                                                                                                                                                                            • 7.2 Nuclear Reactions
                                                                                                                                                                                                                              • 7.2.1 Atomic Mass Unit
                                                                                                                                                                                                                                • 7.2.2 Mass Defect & Nuclear Binding Energy
                                                                                                                                                                                                                                  • 7.2.3 Nuclear Fission & Fusion
                                                                                                                                                                                                                                    • 7.2.4 Binding Energy per Nucleon Curve
                                                                                                                                                                                                                                    • 7.3 The Structure of Matter
                                                                                                                                                                                                                                      • 7.3.1 Discovery of the Nucleus
                                                                                                                                                                                                                                        • 7.3.2 Quarks & Leptons
                                                                                                                                                                                                                                          • 7.3.3 Hadrons, Baryons & Mesons
                                                                                                                                                                                                                                            • 7.3.4 Particle Conservation Laws
                                                                                                                                                                                                                                              • 7.3.5 Fundamental Forces
                                                                                                                                                                                                                                                • 7.3.6 Feynman Diagrams & Confinement
                                                                                                                                                                                                                                                  • 7.3.7 The Standard Model of Particle Physics
                                                                                                                                                                                                                                                • 8. Energy Production
                                                                                                                                                                                                                                                  • 8.1 Energy Sources
                                                                                                                                                                                                                                                    • 8.1.1 Specific Energy
                                                                                                                                                                                                                                                      • 8.1.2 Sankey Diagrams
                                                                                                                                                                                                                                                        • 8.1.3 Primary & Secondary Energy Sources
                                                                                                                                                                                                                                                          • 8.1.4 Energy Resources
                                                                                                                                                                                                                                                            • 8.1.5 Energy Generation
                                                                                                                                                                                                                                                              • 8.1.6 Safety Issues in Nuclear Power
                                                                                                                                                                                                                                                              • 8.2 Thermal Energy Transfer
                                                                                                                                                                                                                                                                • 8.2.1 Conduction, Convection & Thermal Radiation
                                                                                                                                                                                                                                                                  • 8.2.2 Black-Body Radiation
                                                                                                                                                                                                                                                                    • 8.2.3 The Solar Constant, Albedo & Emissivity
                                                                                                                                                                                                                                                                      • 8.2.4 The Greenhouse Effect
                                                                                                                                                                                                                                                                        • 8.2.5 Earth's Surface–Atmosphere System
                                                                                                                                                                                                                                                                      • 9. Wave Phenomena (HL only)
                                                                                                                                                                                                                                                                        • 9.1 Simple Harmonic Motion
                                                                                                                                                                                                                                                                          • 9.1.1 The Defining Equation of SHM
                                                                                                                                                                                                                                                                            • 9.1.2 Energy Changes in SHM
                                                                                                                                                                                                                                                                              • 9.1.3 Calculating Energy Changes in SHM
                                                                                                                                                                                                                                                                                • 9.1.4 Examples of SHM
                                                                                                                                                                                                                                                                                • 9.2 Single-Slit Diffraction
                                                                                                                                                                                                                                                                                  • 9.2.1 The Nature of Single-Slit Diffraction
                                                                                                                                                                                                                                                                                    • 9.2.2 Intensity of Interference Maxima & Minima
                                                                                                                                                                                                                                                                                    • 9.3 Interference
                                                                                                                                                                                                                                                                                      • 9.3.1 Young’s Double-Slit Experiment
                                                                                                                                                                                                                                                                                        • 9.3.2 Two-Slit Interference Patterns
                                                                                                                                                                                                                                                                                          • 9.3.3 Diffraction Grating Patterns
                                                                                                                                                                                                                                                                                            • 9.3.4 The Diffraction Grating Equation
                                                                                                                                                                                                                                                                                              • 9.3.5 Thin Film Interference
                                                                                                                                                                                                                                                                                              • 9.4 Resolution
                                                                                                                                                                                                                                                                                                • 9.4.1 The Rayleigh Criterion
                                                                                                                                                                                                                                                                                                  • 9.4.2 Rayleigh Criterion Calculations
                                                                                                                                                                                                                                                                                                    • 9.4.3 Resolvance of Diffraction Gratings
                                                                                                                                                                                                                                                                                                    • 9.5 Doppler Effect
                                                                                                                                                                                                                                                                                                      • 9.5.1 The Doppler Effect
                                                                                                                                                                                                                                                                                                        • 9.5.2 Uses of The Doppler Effect
                                                                                                                                                                                                                                                                                                          • 9.5.3 The Doppler Equation
                                                                                                                                                                                                                                                                                                        • 10. Fields (HL only)
                                                                                                                                                                                                                                                                                                          • 10.1 Describing Fields
                                                                                                                                                                                                                                                                                                            • 10.1.1 Gravitational & Electrostatic Fields
                                                                                                                                                                                                                                                                                                              • 10.1.2 Gravitational & Electrostatic Field Lines
                                                                                                                                                                                                                                                                                                                • 10.1.3 Gravitational & Electrostatic Potential
                                                                                                                                                                                                                                                                                                                  • 10.1.4 Equipotential Surfaces
                                                                                                                                                                                                                                                                                                                  • 10.2 Fields at Work
                                                                                                                                                                                                                                                                                                                    • 10.2.1 Potential & Potential Energy
                                                                                                                                                                                                                                                                                                                      • 10.2.2 Potential Energy Calculations
                                                                                                                                                                                                                                                                                                                        • 10.2.3 Potential Gradient & Difference
                                                                                                                                                                                                                                                                                                                          • 10.2.4 Potential in a Charged Sphere
                                                                                                                                                                                                                                                                                                                            • 10.2.5 Escape Speed
                                                                                                                                                                                                                                                                                                                              • 10.2.6 Orbital Motion, Speed & Energy
                                                                                                                                                                                                                                                                                                                                • 10.2.7 Forces & Inverse-Square Law Behaviour
                                                                                                                                                                                                                                                                                                                                  • 10.2.8 Forces on Charges & Masses
                                                                                                                                                                                                                                                                                                                                • 11. Electromagnetic Induction (HL only)
                                                                                                                                                                                                                                                                                                                                  • 11.1 Electromagnetic Induction
                                                                                                                                                                                                                                                                                                                                    • 11.1.1 Emf, Magnetic Flux & Magnetic Flux Linkage
                                                                                                                                                                                                                                                                                                                                      • 11.1.2 Induced Emf
                                                                                                                                                                                                                                                                                                                                        • 11.1.3 Faraday’s Law
                                                                                                                                                                                                                                                                                                                                          • 11.1.4 Lenz’s Law
                                                                                                                                                                                                                                                                                                                                          • 11.2 Power Generation & Transmission
                                                                                                                                                                                                                                                                                                                                            • 11.2.1 AC Generators
                                                                                                                                                                                                                                                                                                                                              • 11.2.2 Root-Mean-Square Current & Voltage
                                                                                                                                                                                                                                                                                                                                                • 11.2.3 Step-Up & Step-Down Transformers
                                                                                                                                                                                                                                                                                                                                                  • 11.2.4 Transformer Calculations
                                                                                                                                                                                                                                                                                                                                                    • 11.2.5 AC Electrical Power Distribution
                                                                                                                                                                                                                                                                                                                                                      • 11.2.6 Diode Bridges
                                                                                                                                                                                                                                                                                                                                                        • 11.2.7 Investigating Diode Bridges
                                                                                                                                                                                                                                                                                                                                                          • 11.2.8 Rectification
                                                                                                                                                                                                                                                                                                                                                            • 11.2.9 Capacitors & Diode Bridges
                                                                                                                                                                                                                                                                                                                                                            • 11.3 Capacitance
                                                                                                                                                                                                                                                                                                                                                              • 11.3.1 Capacitance
                                                                                                                                                                                                                                                                                                                                                                • 11.3.2 Dielectric Materials
                                                                                                                                                                                                                                                                                                                                                                  • 11.3.3 Capacitors in Series & Parallel
                                                                                                                                                                                                                                                                                                                                                                    • 11.3.4 The Time Constant
                                                                                                                                                                                                                                                                                                                                                                      • 11.3.5 Energy Stored in a Capacitor
                                                                                                                                                                                                                                                                                                                                                                        • 11.3.6 Capacitor Charge & Discharge
                                                                                                                                                                                                                                                                                                                                                                          • 11.3.7 Discharge Calculations
                                                                                                                                                                                                                                                                                                                                                                        • 12. Quantum & Nuclear Physics (HL only)
                                                                                                                                                                                                                                                                                                                                                                          • 12.1 The Interaction of Matter with Radiation
                                                                                                                                                                                                                                                                                                                                                                            • 12.1.1 Photons
                                                                                                                                                                                                                                                                                                                                                                              • 12.1.2 The Photoelectric Effect
                                                                                                                                                                                                                                                                                                                                                                                • 12.1.3 Observing the Photoelectric Effect
                                                                                                                                                                                                                                                                                                                                                                                  • 12.1.4 Solving Photoelectric Problems
                                                                                                                                                                                                                                                                                                                                                                                    • 12.1.5 Matter Waves
                                                                                                                                                                                                                                                                                                                                                                                      • 12.1.6 Pair Production & Annihilation
                                                                                                                                                                                                                                                                                                                                                                                        • 12.1.7 Quantization of Angular Momentum
                                                                                                                                                                                                                                                                                                                                                                                          • 12.1.8 The Wave Function
                                                                                                                                                                                                                                                                                                                                                                                            • 12.1.9 The Uncertainty Principle
                                                                                                                                                                                                                                                                                                                                                                                              • 12.1.10 Tunnelling
                                                                                                                                                                                                                                                                                                                                                                                              • 12.2 Nuclear Physics
                                                                                                                                                                                                                                                                                                                                                                                                • 12.2.1 Rutherford Scattering & Nuclear Radius
                                                                                                                                                                                                                                                                                                                                                                                                  • 12.2.2 Nuclear Scattering
                                                                                                                                                                                                                                                                                                                                                                                                    • 12.2.3 Deviations from Rutherford Scattering
                                                                                                                                                                                                                                                                                                                                                                                                      • 12.2.4 Nuclear Energy Levels
                                                                                                                                                                                                                                                                                                                                                                                                        • 12.2.5 The Neutrino
                                                                                                                                                                                                                                                                                                                                                                                                          • 12.2.6 The Law of Radioactive Decay
                                                                                                                                                                                                                                                                                                                                                                                                            • 12.2.7 Measuring Half-Life
                                                                                                                                                                                                                                                                                                                                                                                                          Katie Moon

                                                                                                                                                                                                                                                                                                                                                                                                          Author: Katie

                                                                                                                                                                                                                                                                                                                                                                                                          Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.


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