D.2 Electric and magnetic fields

Calculate the work done to bring a small charge q from infinity to point C.

Data given:

Q = 2.0 × 10⁻³ C,

q = 4.0 × 10⁻⁹ C

D = 1.2 m

Calculate the work done to bring a small charge q from infinity to point C.

Data given:

Q = 2.0 × 10⁻³ C,

q = 4.0 × 10⁻⁹ C

D = 1.2 m

Calculate the work done to bring a small charge q from infinity to point C.

Data given:

Q = 2.0 × 10⁻³ C,

q = 4.0 × 10⁻⁹ C

D = 1.2 m

An electric field is established between two electrodes separated by distance d, held at a potential difference of V. A charged particle in this field experiences a force F.

What is the charge on the particle?

A.  $\frac{d}{FV}$

B.  $\frac{FV}{d}$

C.  $\frac{V}{Fd}$

D.  $\frac{Fd}{V}$

An electric field is established between two electrodes separated by distance d, held at a potential difference of V. A charged particle in this field experiences a force F.

What is the charge on the particle?

A.  $\frac{d}{FV}$

B.  $\frac{FV}{d}$

C.  $\frac{V}{Fd}$

D.  $\frac{Fd}{V}$

The diagram shows field lines for an electrostatic field. X and Y are two points on the same field line.

Outline which of the two points has the larger electric potential.

The diagram shows field lines for an electrostatic field. X and Y are two points on the same field line.

Outline which of the two points has the larger electric potential.

The diagram shows field lines for an electrostatic field. X and Y are two points on the same field line.

Outline which of the two points has the larger electric potential.

Show that the electric charge on the oil drop is given by

$q=\frac{{\rho }_{o}gV}{E}$

where ${\rho }_o$ is the density of oil and $V$ is the volume of the oil drop.

Show that the electric charge on the oil drop is given by

$q=\frac{{\rho }_{o}gV}{E}$

where ${\rho }_o$ is the density of oil and $V$ is the volume of the oil drop.

Show that the electric charge on the oil drop is given by

$q=\frac{{\rho }_{o}gV}{E}$

where ${\rho }_o$ is the density of oil and $V$ is the volume of the oil drop.

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A charged rod is brought near an initially neutral metal sphere without touching it.

When the sphere is grounded (earthed), there is an electric current for a short time from the sphere to the ground.

The ground connection is then removed.

What are the charge on the rod and the charge induced on the sphere when the connection is removed?

A particle with a charge ne is accelerated through a potential difference V.

What is the magnitude of the work done on the particle?

A. $eV$

B. $neV$

C. $\frac{nV}{e}$

D. $\frac{eV}{n}$

A particle with a charge ne is accelerated through a potential difference V.

What is the magnitude of the work done on the particle?

A. $eV$

B. $neV$

C. $\frac{nV}{e}$

D. $\frac{eV}{n}$

The diagram shows some of the electric field lines for two fixed, charged particles X and Y.

The magnitude of the charge on X is $Q$ and that on Y is $q$. The distance between X and Y is 0.600 m. The distance between P and Y is 0.820 m.

At P the electric field is zero. Determine, to one significant figure, the ratio $\frac{Q}{q}$.

The diagram shows some of the electric field lines for two fixed, charged particles X and Y.

The magnitude of the charge on X is $Q$ and that on Y is $q$. The distance between X and Y is 0.600 m. The distance between P and Y is 0.820 m.

At P the electric field is zero. Determine, to one significant figure, the ratio $\frac{Q}{q}$.

The diagram shows some of the electric field lines for two fixed, charged particles X and Y.

The magnitude of the charge on X is $Q$ and that on Y is $q$. The distance between X and Y is 0.600 m. The distance between P and Y is 0.820 m.

At P the electric field is zero. Determine, to one significant figure, the ratio $\frac{Q}{q}$.

The force acting between two point charges is $F$ when the separation of the charges is $x$. What is the force between the charges when the separation is increased to $3x$?

A. $\frac{F}{3}$

B. $\frac{F}{3x^2}$

C. $\frac{F}{9}$

D. $\frac{F}{9x^2}$

The force acting between two point charges is $F$ when the separation of the charges is $x$. What is the force between the charges when the separation is increased to $3x$?

A. $\frac{F}{3}$

B. $\frac{F}{3x^2}$

C. $\frac{F}{9}$

D. $\frac{F}{9x^2}$

Show that the electric field strength due to the point charge at the position of the electron is 3.4 × 10⁸ N C^–1.

Show that the electric field strength due to the point charge at the position of the electron is 3.4 × 10⁸ N C^–1.

Show that the electric field strength due to the point charge at the position of the electron is 3.4 × 10⁸ N C^–1.

Calculate the magnitude of the initial acceleration of the electron.

Calculate the magnitude of the initial acceleration of the electron.

Calculate the magnitude of the initial acceleration of the electron.

The graph shows the variation of electric field strength $E$ with distance $r$ from a point charge.

The shaded area X is the area under the graph between two separations $r_1$ and $r_2$ from the charge.

What is X?

A.  The electric field average between $r_1$ and $r_2$

B.  The electric potential difference between $r_1$ and $r_2$

C.  The work done in moving a charge from $r_1$ to $r_2$

D.  The work done in moving a charge from $r_2$ to $r_1$ 

The graph shows the variation of electric field strength $E$ with distance $r$ from a point charge.

The shaded area X is the area under the graph between two separations $r_1$ and $r_2$ from the charge.

What is X?

A.  The electric field average between $r_1$ and $r_2$

B.  The electric potential difference between $r_1$ and $r_2$

C.  The work done in moving a charge from $r_1$ to $r_2$

D.  The work done in moving a charge from $r_2$ to $r_1$ 

Explain why the electric potential decreases from A to B.

Explain why the electric potential decreases from A to B.

Explain why the electric potential decreases from A to B.

Draw, on the axes, the variation of electric potential $V$ with distance $r$ from the centre of the sphere.

Draw, on the axes, the variation of electric potential $V$ with distance $r$ from the centre of the sphere.

Draw, on the axes, the variation of electric potential $V$ with distance $r$ from the centre of the sphere.

Calculate the electric potential difference between points A and B.

Calculate the electric potential difference between points A and B.

Calculate the electric potential difference between points A and B.

Determine the charge $Q$ of the sphere.

Determine the charge $Q$ of the sphere.

Determine the charge $Q$ of the sphere.

The points X and Y are in a uniform electric field of strength $E$. The distance OX is $x$ and the distance OY is $y$.

What is the magnitude of the change in electric potential between X and Y?

A.  $Ex$

B.  $Ey$

C.  $E(x + y)$

D.  $E\sqrt{x^2 + y^2}$

The points X and Y are in a uniform electric field of strength $E$. The distance OX is $x$ and the distance OY is $y$.

What is the magnitude of the change in electric potential between X and Y?

A.  $Ex$

B.  $Ey$

C.  $E(x + y)$

D.  $E\sqrt{x^2 + y^2}$

A charge +Q and a charge −2Q are a distance 3x apart. Point P is on the line joining the charges, at a distance x from +Q.

The magnitude of the electric field produced at P by the charge +Q alone is $E$.

What is the total electric field at P?

A.  $\frac{E}{2}$ to the right

B.  $\frac{E}{2}$ to the left

C.  $\frac{3E}{2}$ to the right

D.  $\frac{3E}{2}$ to the left

A charge +Q and a charge −2Q are a distance 3x apart. Point P is on the line joining the charges, at a distance x from +Q.

The magnitude of the electric field produced at P by the charge +Q alone is $E$.

What is the total electric field at P?

A.  $\frac{E}{2}$ to the right

B.  $\frac{E}{2}$ to the left

C.  $\frac{3E}{2}$ to the right

D.  $\frac{3E}{2}$ to the left

Show that the magnitude of the resultant electric field at P is 3 MN C⁻¹

Show that the magnitude of the resultant electric field at P is 3 MN C⁻¹

Show that the magnitude of the resultant electric field at P is 3 MN C⁻¹

Show that the charge on the surface of the sphere is +18 μC.

Show that the charge on the surface of the sphere is +18 μC.

Show that the charge on the surface of the sphere is +18 μC.

Predict the charge on each sphere.

Predict the charge on each sphere.

Predict the charge on each sphere.

Determine the force on Q at the instant it is released.

Determine the force on Q at the instant it is released.

Determine the force on Q at the instant it is released.

A charged sphere in a gravitational field is initially stationary between two parallel metal plates. There is a potential difference V between the plates.

Three changes can be made:

I.   Increase the separation of the metal plates
II.  Increase V
III. Apply a magnetic field into the plane of the paper

What changes made separately will cause the charged sphere to accelerate?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A charged sphere in a gravitational field is initially stationary between two parallel metal plates. There is a potential difference V between the plates.

Three changes can be made:

I.   Increase the separation of the metal plates
II.  Increase V
III. Apply a magnetic field into the plane of the paper

What changes made separately will cause the charged sphere to accelerate?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

Four particles, two of charge +Q and two of charge −Q, are positioned on the $x$-axis as shown. A particle P with a positive charge is placed on the $y$-axis. What is the direction of the net electrostatic force on this particle?

Four particles, two of charge +Q and two of charge −Q, are positioned on the $x$-axis as shown. A particle P with a positive charge is placed on the $y$-axis. What is the direction of the net electrostatic force on this particle?

P and Q are two opposite point charges. The force F acting on P due to Q and the electric field strength E at P are shown.

Which diagram shows the force on Q due to P and the electric field strength at Q?

P and Q are two opposite point charges. The force F acting on P due to Q and the electric field strength E at P are shown.

Which diagram shows the force on Q due to P and the electric field strength at Q?

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 $X$. What is the magnitude of the resultant magnetic field at Q due to both wires?

A.  $\frac{X}{2}$

B.  $X$

C.  $X\sqrt{2}$

D.  $2X$

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 $X$. What is the magnitude of the resultant magnetic field at Q due to both wires?

A.  $\frac{X}{2}$

B.  $X$

C.  $X\sqrt{2}$

D.  $2X$

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 $X$. What is the magnitude of the resultant magnetic field at Q due to both wires?

A.  $\frac{X}{2}$

B.  $X$

C.  $X\sqrt{2}$

D.  $2X$

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 $X$. What is the magnitude of the resultant magnetic field at Q due to both wires?

A.  $\frac{X}{2}$

B.  $X$

C.  $X\sqrt{2}$

D.  $2X$

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?

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?

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?

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?

Calculate the work done to bring a small charge q from infinity to point C.

Data given:

Q = 2.0 × 10⁻³ C,

q = 4.0 × 10⁻⁹ C

D = 1.2 m

Calculate the work done to bring a small charge q from infinity to point C.

Data given:

Q = 2.0 × 10⁻³ C,

q = 4.0 × 10⁻⁹ C

D = 1.2 m

Calculate the work done to bring a small charge q from infinity to point C.

Data given:

Q = 2.0 × 10⁻³ C,

q = 4.0 × 10⁻⁹ C

D = 1.2 m