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A.1 – The beginnings of relativity
Description
Nature of science:
Paradigm shift: The fundamental fact that the speed of light is constant for all inertial observers has far-reaching consequences about our understanding of space and time. Ideas about space and time that went unchallenged for more than 2,000 years were shown to be false. The extension of the principle of relativity to accelerated frames of reference leads to the revolutionary idea of general relativity that the mass and energy that spacetime contains determine the geometry of spacetime. (2.3)
Understandings:
- Reference frames
- Galilean relativity and Newton’s postulates concerning time and space
- Maxwell and the constancy of the speed of light
- Forces on a charge or current
Applications and skills:
- Using the Galilean transformation equations
- Determining whether a force on a charge or current is electric or magnetic in a given frame of reference
- Determining the nature of the fields observed by different observers
Guidance:
- Maxwell’s equations do not need to be described
- Qualitative treatment of electric and magnetic fields as measured by observers in relative motion. Examples will include a charge moving in a magnetic field or two charged particles moving with parallel velocities. Students will be asked to analyse these motions from the point of view of observers at rest with respect to the particles and observers at rest with respect to the magnetic field.
Data booklet reference:
Theory of knowledge:
- When scientists claim a new direction in thinking requires a paradigm shift in how we observe the universe, how do we ensure their claims are valid?
Aims:
- Aim 3: this sub-topic is the cornerstone of developments that followed in relativity and modern physics
Directly related questions
- 20N.3.SL.TZ0.3c(ii): A second observer moves at the drift velocity of the electron current in the wires. Discuss how...
- 20N.3.SL.TZ0.3c(ii): A second observer moves at the drift velocity of the electron current in the wires. Discuss how...
- 20N.3.SL.TZ0.c(ii): A second observer moves at the drift velocity of the electron current in the wires. Discuss how...
- 17N.3.SL.TZ0.4: Outline the conclusion from Maxwell’s work on electromagnetism that led to one of the postulates...
- 17N.3.SL.TZ0.4: Outline the conclusion from Maxwell’s work on electromagnetism that led to one of the postulates...
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18M.3.SL.TZ1.3b.ii:
Deduce whether the overall field around the wire is electric, magnetic or a combination of both according to observer Y.
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18M.3.SL.TZ1.3b.ii:
Deduce whether the overall field around the wire is electric, magnetic or a combination of both according to observer Y.
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18M.3.SL.TZ1.b.ii:
Deduce whether the overall field around the wire is electric, magnetic or a combination of both according to observer Y.
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18M.3.SL.TZ2.3a.i:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Galilean transformation.
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18M.3.SL.TZ2.3a.i:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Galilean transformation.
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18M.3.SL.TZ2.a.i:
Calculate, for the reference frame of rocket A, the speed of rocket B according to the Galilean transformation.
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18N.3.SL.TZ0.3b.i:
explain why the time coordinate of E in frame S is .
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18N.3.SL.TZ0.3b.i:
explain why the time coordinate of E in frame S is .
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18N.3.SL.TZ0.b.i:
explain why the time coordinate of E in frame S is .
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18N.3.SL.TZ0.3b.ii:
hence show that the space coordinate of E in frame S is .
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18N.3.SL.TZ0.3b.ii:
hence show that the space coordinate of E in frame S is .
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18N.3.SL.TZ0.b.ii:
hence show that the space coordinate of E in frame S is .
- 18N.3.SL.TZ0.3a: State what is meant by a reference frame.
- 18N.3.SL.TZ0.3a: State what is meant by a reference frame.
- 18N.3.SL.TZ0.a: State what is meant by a reference frame.
- 19M.3.SL.TZ2.5b: Explain why there is no magnetic force on each proton in its own rest frame.
- 19M.3.SL.TZ2.5b: Explain why there is no magnetic force on each proton in its own rest frame.
- 19M.3.SL.TZ2.b: Explain why there is no magnetic force on each proton in its own rest frame.
- 19M.3.SL.TZ2.5c: Explain why there must be a resultant repulsive force on the protons in all reference frames.
- 19M.3.SL.TZ2.5c: Explain why there must be a resultant repulsive force on the protons in all reference frames.
- 19M.3.SL.TZ2.c: Explain why there must be a resultant repulsive force on the protons in all reference frames.
- 19M.3.SL.TZ2.4ai: Define an inertial reference frame.
- 19M.3.SL.TZ2.4ai: Define an inertial reference frame.
- 19M.3.SL.TZ2.ai: Define an inertial reference frame.
- 19M.3.SL.TZ2.5a: Outline why there is an attractive magnetic force on each proton in the laboratory frame.
- 19M.3.SL.TZ2.5a: Outline why there is an attractive magnetic force on each proton in the laboratory frame.
- 19M.3.SL.TZ2.a: Outline why there is an attractive magnetic force on each proton in the laboratory frame.
- 19M.3.SL.TZ2.4aii: As the spaceship passes the Earth it emits a flash of light that travels in the same direction as...
- 19M.3.SL.TZ2.4aii: As the spaceship passes the Earth it emits a flash of light that travels in the same direction as...
- 19M.3.SL.TZ2.aii: As the spaceship passes the Earth it emits a flash of light that travels in the same direction as...
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19M.3.SL.TZ2.4b:
Use your answer to (a)(ii) to describe the paradigm shift that Einstein’s theory of special relativity produced.
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19M.3.SL.TZ2.4b:
Use your answer to (a)(ii) to describe the paradigm shift that Einstein’s theory of special relativity produced.
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19M.3.SL.TZ2.b:
Use your answer to (a)(ii) to describe the paradigm shift that Einstein’s theory of special relativity produced.
- 19N.3.SL.TZ0.3b(i): State the nature of the force on the particle P in the reference frame of the laboratory.
- 19N.3.SL.TZ0.3b(i): State the nature of the force on the particle P in the reference frame of the laboratory.
- 19N.3.SL.TZ0.b(i): State the nature of the force on the particle P in the reference frame of the laboratory.
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19N.3.SL.TZ0.3b(ii):
Deduce, using your answer to part (a), the nature of the force that acts on the particle P in the rest frame of P.
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19N.3.SL.TZ0.3b(ii):
Deduce, using your answer to part (a), the nature of the force that acts on the particle P in the rest frame of P.
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19N.3.SL.TZ0.b(ii):
Deduce, using your answer to part (a), the nature of the force that acts on the particle P in the rest frame of P.
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18M.3.SL.TZ1.3a:
State whether the field around the wire according to observer X is electric, magnetic or a combination of both.
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18M.3.SL.TZ1.3a:
State whether the field around the wire according to observer X is electric, magnetic or a combination of both.
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18M.3.SL.TZ1.a:
State whether the field around the wire according to observer X is electric, magnetic or a combination of both.
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18M.3.SL.TZ1.4a.i:
Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.
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18M.3.SL.TZ1.4a.i:
Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.
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18M.3.SL.TZ1.a.i:
Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.
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18M.3.SL.TZ1.4a.ii:
Deduce why only a small fraction of the total number of muons created is expected to be detected at ground level according to Galilean relativity.
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18M.3.SL.TZ1.4a.ii:
Deduce why only a small fraction of the total number of muons created is expected to be detected at ground level according to Galilean relativity.
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18M.3.SL.TZ1.a.ii:
Deduce why only a small fraction of the total number of muons created is expected to be detected at ground level according to Galilean relativity.
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18N.3.SL.TZ0.4b.i:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest in the rocket.
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18N.3.SL.TZ0.4b.i:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest in the rocket.
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18N.3.SL.TZ0.b.i:
Determine the time it takes the probe to reach the front of the rocket according to an observer at rest in the rocket.
- 19M.3.SL.TZ1.3a: State the speed of the flash of light according to an observer on the ground using Galilean...
- 19M.3.SL.TZ1.3a: State the speed of the flash of light according to an observer on the ground using Galilean...
- 19M.3.SL.TZ1.a: State the speed of the flash of light according to an observer on the ground using Galilean...
- 19M.3.SL.TZ1.3b: State the speed of the flash of light according to an observer on the ground using Maxwell’s...
- 19M.3.SL.TZ1.3b: State the speed of the flash of light according to an observer on the ground using Maxwell’s...
- 19M.3.SL.TZ1.b: State the speed of the flash of light according to an observer on the ground using Maxwell’s...
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19M.3.SL.TZ1.4a.i:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to Newtonian mechanics.
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19M.3.SL.TZ1.4a.i:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to Newtonian mechanics.
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19M.3.SL.TZ1.a.i:
Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to Newtonian mechanics.
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19N.3.SL.TZ0.3b(iii):
Explain how the force in part (b)(ii) arises.
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19N.3.SL.TZ0.3b(iii):
Explain how the force in part (b)(ii) arises.
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19N.3.SL.TZ0.b(iii):
Explain how the force in part (b)(ii) arises.
- 20N.3.SL.TZ0.3a: Maxwell’s equations led to the constancy of the speed of light. Identify what Maxwell’s equations...
- 20N.3.SL.TZ0.3a: Maxwell’s equations led to the constancy of the speed of light. Identify what Maxwell’s equations...
- 20N.3.SL.TZ0.a: Maxwell’s equations led to the constancy of the speed of light. Identify what Maxwell’s equations...
- 20N.3.SL.TZ0.3b: State a postulate that is the same for both special relativity and Galilean relativity.
- 20N.3.SL.TZ0.3b: State a postulate that is the same for both special relativity and Galilean relativity.
- 20N.3.SL.TZ0.b: State a postulate that is the same for both special relativity and Galilean relativity.
- 20N.3.SL.TZ0.3c(i): Identify the nature of the attractive force recorded by an observer stationary with respect to...
- 20N.3.SL.TZ0.3c(i): Identify the nature of the attractive force recorded by an observer stationary with respect to...
- 20N.3.SL.TZ0.c(i): Identify the nature of the attractive force recorded by an observer stationary with respect to...
- 20N.3.SL.TZ0.4a: The Lorentz transformations assume that the speed of light is constant. Outline what the Galilean...
- 20N.3.SL.TZ0.4a: The Lorentz transformations assume that the speed of light is constant. Outline what the Galilean...
- 20N.3.SL.TZ0.a: The Lorentz transformations assume that the speed of light is constant. Outline what the Galilean...
- 23M.1.HL.TZ1.15: Two positive charges of magnitude q and 2q are fixed as shown. At which position is the electric...
- 23M.1.SL.TZ1.18: Two positive charges of magnitude q and 2q are fixed as shown. At which position is the electric...
- 23M.1.SL.TZ1.18: Two positive charges of magnitude q and 2q are fixed as shown. At which position is the electric...
- 23M.1.HL.TZ1.15: Two positive charges of magnitude q and 2q are fixed as shown. At which position is the electric...
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23M.1.HL.TZ1.17:
Three lamps (X, Y and Z) are connected as shown in the circuit. The emf of the cell is 20 V. The internal resistance of the cell is negligible. The power dissipated by X, Y and Z is 10 W, 20 W and 20 W respectively.
What is the voltage across Lamp X and Lamp Y?
Lamp X Lamp Y A. 16 V 4 V B. 4 V 16 V C. 4 V 8 V D. 16 V 16 V -
23M.1.HL.TZ1.17:
Three lamps (X, Y and Z) are connected as shown in the circuit. The emf of the cell is 20 V. The internal resistance of the cell is negligible. The power dissipated by X, Y and Z is 10 W, 20 W and 20 W respectively.
What is the voltage across Lamp X and Lamp Y?
Lamp X Lamp Y A. 16 V 4 V B. 4 V 16 V C. 4 V 8 V D. 16 V 16 V -
23M.1.HL.TZ1.16:
P and Q are two conductors of the same material connected in series. Q has a diameter twice that of P.
What is ?
A. 4B. 2
C.
D.
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23M.1.HL.TZ1.16:
P and Q are two conductors of the same material connected in series. Q has a diameter twice that of P.
What is ?
A. 4B. 2
C.
D.
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23M.1.HL.TZ1.31:
A negatively charged particle is stationary halfway between two horizontal charged plates. The plates are separated by a distance d with potential difference V between them.
What is the magnitude of the electric field and direction of the electric field at the position of the particle?
Magnitude of
electric fieldDirection of
electric fieldA. up B. up C. down D. down -
23M.1.HL.TZ1.31:
A negatively charged particle is stationary halfway between two horizontal charged plates. The plates are separated by a distance d with potential difference V between them.
What is the magnitude of the electric field and direction of the electric field at the position of the particle?
Magnitude of
electric fieldDirection of
electric fieldA. up B. up C. down D. down -
23M.1.HL.TZ1.19:
P and R are parallel wires carrying the same current into the plane of the paper. P and R are equidistant from a point Q. The line PQ is perpendicular to the line RQ.
The magnetic field due to P at Q is . What is the magnitude of the resultant magnetic field at Q due to both wires?
A.B.
C.
D.
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23M.1.HL.TZ1.19:
P and R are parallel wires carrying the same current into the plane of the paper. P and R are equidistant from a point Q. The line PQ is perpendicular to the line RQ.
The magnetic field due to P at Q is . What is the magnitude of the resultant magnetic field at Q due to both wires?
A.B.
C.
D.
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23M.2.SL.TZ1.4a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.
R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.
The current in P is 0.40 A.
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23M.2.HL.TZ1.4a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.
R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.
The current in P is 0.40 A.
-
23M.2.SL.TZ1.4a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.
R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.
The current in P is 0.40 A.
-
23M.2.SL.TZ1.a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.
R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.
The current in P is 0.40 A.
-
23M.2.HL.TZ1.4a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.
R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.
The current in P is 0.40 A.
-
23M.2.HL.TZ1.a:
A cell of negligible internal resistance and electromotive force (emf) 6.0 V is connected to three resistors R, P and Q.
R is an ohmic resistor. The I-V characteristics of P and Q are shown in the graph.
The current in P is 0.40 A.
- 23M.2.HL.TZ1.6a: The centres of two identical fixed conducting spheres each of charge +Q are separated by a...
- 23M.2.HL.TZ1.6a: The centres of two identical fixed conducting spheres each of charge +Q are separated by a...
- 23M.2.HL.TZ1.a: The centres of two identical fixed conducting spheres each of charge +Q are separated by a...
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23M.1.SL.TZ1.19:
X and Y are two conductors with the same diameter, made from the same material. Y is twice the length of X. They are connected in series to a cell of emf ε.
X dissipates power P.
What is the power dissipated by Y?
A.B. P
C. 2P
D. 4P
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23M.1.SL.TZ1.19:
X and Y are two conductors with the same diameter, made from the same material. Y is twice the length of X. They are connected in series to a cell of emf ε.
X dissipates power P.
What is the power dissipated by Y?
A.B. P
C. 2P
D. 4P
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23M.1.SL.TZ1.20:
Four identical lamps are connected in a circuit. The current through lamp L is I.
The lamps are rearranged using the same cell.
What is the current through L?
A.B.
C. I
D. 2I
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23M.1.SL.TZ1.20:
Four identical lamps are connected in a circuit. The current through lamp L is I.
The lamps are rearranged using the same cell.
What is the current through L?
A.B.
C. I
D. 2I
- 23M.1.SL.TZ2.19: Three point charges, +Q, +Q and −Q, are fixed at the three corners of a square. What is the...
- 23M.1.HL.TZ2.15: Three point charges, +Q, +Q and −Q, are fixed at the three corners of a square. What is the...
- 23M.1.SL.TZ2.19: Three point charges, +Q, +Q and −Q, are fixed at the three corners of a square. What is the...
- 23M.1.HL.TZ2.15: Three point charges, +Q, +Q and −Q, are fixed at the three corners of a square. What is the...
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23M.2.HL.TZ1.7a:
Explain, by reference to Faraday’s law of electromagnetic induction, why there is an electromotive force (emf) induced in the loop as it leaves the region of magnetic field.
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23M.2.HL.TZ1.7a:
Explain, by reference to Faraday’s law of electromagnetic induction, why there is an electromotive force (emf) induced in the loop as it leaves the region of magnetic field.
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23M.2.HL.TZ1.a:
Explain, by reference to Faraday’s law of electromagnetic induction, why there is an electromotive force (emf) induced in the loop as it leaves the region of magnetic field.
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23M.1.SL.TZ2.20:
Two resistors of equal resistance R are connected with two cells of emf ε and 2ε. Both cells have negligible internal resistance.
What is the current in the resistor labelled X?
A.B.
C.
D.
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23M.1.HL.TZ2.16:
Two resistors of equal resistance R are connected with two cells of emf ε and 2ε. Both cells have negligible internal resistance.
What is the current in the resistor labelled X?
A.B.
C.
D.
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23M.1.SL.TZ2.20:
Two resistors of equal resistance R are connected with two cells of emf ε and 2ε. Both cells have negligible internal resistance.
What is the current in the resistor labelled X?
A.B.
C.
D.
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23M.1.HL.TZ2.16:
Two resistors of equal resistance R are connected with two cells of emf ε and 2ε. Both cells have negligible internal resistance.
What is the current in the resistor labelled X?
A.B.
C.
D.
- 23M.1.HL.TZ2.30: Two spheres have the same positive charge. A point M is midway between the two spheres. Along...
- 23M.1.HL.TZ2.30: Two spheres have the same positive charge. A point M is midway between the two spheres. Along...
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23M.1.SL.TZ2.17:
A variable resistor is connected to a cell with emf ε and internal resistance r as shown. When the current in the circuit is I, the potential difference measured across the terminals of the cell is V.
The resistance of the variable resistor is doubled.
What is true about the current and the potential difference?
Current Potential difference A. greater than greater than V B. less than greater than V C. greater than equal to V D. less than equal to V -
23M.1.SL.TZ2.17:
A variable resistor is connected to a cell with emf ε and internal resistance r as shown. When the current in the circuit is I, the potential difference measured across the terminals of the cell is V.
The resistance of the variable resistor is doubled.
What is true about the current and the potential difference?
Current Potential difference A. greater than greater than V B. less than greater than V C. greater than equal to V D. less than equal to V -
23M.1.SL.TZ2.22:
An electron is accelerated from rest through a potential difference V.
What is the maximum speed of the electron?
A.B.
C.
D.
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23M.1.SL.TZ2.22:
An electron is accelerated from rest through a potential difference V.
What is the maximum speed of the electron?
A.B.
C.
D.
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23M.2.SL.TZ2.4a:
The designers state that the energy transferred by the resistor every second is 15 J.
Calculate the current in the resistor.
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23M.2.HL.TZ2.4a:
The designers state that the energy transferred by the resistor every second is 15 J.
Calculate the current in the resistor.
-
23M.2.HL.TZ2.4a:
The designers state that the energy transferred by the resistor every second is 15 J.
Calculate the current in the resistor.
-
23M.2.HL.TZ2.a:
The designers state that the energy transferred by the resistor every second is 15 J.
Calculate the current in the resistor.
-
23M.2.SL.TZ2.4a:
The designers state that the energy transferred by the resistor every second is 15 J.
Calculate the current in the resistor.
-
23M.2.SL.TZ2.a:
The designers state that the energy transferred by the resistor every second is 15 J.
Calculate the current in the resistor.