5.1 – Electric fields

A metal wire has $n$ free charge carriers per unit volume. The charge on the carrier is $q$. What additional quantity is needed to determine the current per unit area in the wire?

A.  Cross-sectional area of the wire

B.  Drift speed of charge carriers

C.  Potential difference across the wire

D.  Resistivity of the metal

A metal wire has $n$ free charge carriers per unit volume. The charge on the carrier is $q$. What additional quantity is needed to determine the current per unit area in the wire?

A.  Cross-sectional area of the wire

B.  Drift speed of charge carriers

C.  Potential difference across the wire

D.  Resistivity of the metal

Two wires, X and Y, are made from the same metal. The wires are connected in series. The radius of X is twice that of Y. The carrier drift speed in X is v_X and in Y it is v_Y.

What is the value of the ratio $\frac{{\text{v}}_{\text{X}}}{{\text{v}}_{\text{Y}}}$?

A. 0.25

B. 0.50

C. 2.00

D. 4.00

Two wires, X and Y, are made from the same metal. The wires are connected in series. The radius of X is twice that of Y. The carrier drift speed in X is v_X and in Y it is v_Y.

What is the value of the ratio $\frac{{\text{v}}_{\text{X}}}{{\text{v}}_{\text{Y}}}$?

A. 0.25

B. 0.50

C. 2.00

D. 4.00

The charge on the ball is 1.2 × 10⁻⁶C. Determine σ.

The charge on the ball is 1.2 × 10⁻⁶C. Determine σ.

The charge on the ball is 1.2 × 10⁻⁶C. Determine σ.

The centre of the ball, still carrying a charge of $1.2\times {10}^{-6} \text{C}$, is now placed $0.40 \text{m}$ from a point charge Q. The charge on the ball acts as a point charge at the centre of the ball.

P is the point on the line joining the charges where the electric field strength is zero.
The distance PQ is $0.22 \text{m}$.

Calculate the charge on Q. State your answer to an appropriate number of significant figures.

The centre of the ball, still carrying a charge of $1.2\times {10}^{-6} \text{C}$, is now placed $0.40 \text{m}$ from a point charge Q. The charge on the ball acts as a point charge at the centre of the ball.

P is the point on the line joining the charges where the electric field strength is zero.
The distance PQ is $0.22 \text{m}$.

Calculate the charge on Q. State your answer to an appropriate number of significant figures.

The centre of the ball, still carrying a charge of $1.2\times {10}^{-6} \text{C}$, is now placed $0.40 \text{m}$ from a point charge Q. The charge on the ball acts as a point charge at the centre of the ball.

P is the point on the line joining the charges where the electric field strength is zero.
The distance PQ is $0.22 \text{m}$.

Calculate the charge on Q. State your answer to an appropriate number of significant figures.

Show that $\frac{v}{E}=\frac{1}{ne\rho }$.

Show that $\frac{v}{E}=\frac{1}{ne\rho }$.

Show that $\frac{v}{E}=\frac{1}{ne\rho }$.

An ion of charge +Q moves vertically upwards through a small distance s in a uniform vertical electric field. The electric field has a strength E and its direction is shown in the diagram.

What is the electric potential difference between the initial and final position of the ion?

A.     $\frac{EQ}{s}$

B.     EQs

C.     Es

D.     $\frac{E}{s}$

An ion of charge +Q moves vertically upwards through a small distance s in a uniform vertical electric field. The electric field has a strength E and its direction is shown in the diagram.

What is the electric potential difference between the initial and final position of the ion?

A.     $\frac{EQ}{s}$

B.     EQs

C.     Es

D.     $\frac{E}{s}$

Determine the electric field strength E.

Determine the electric field strength E.

Determine the electric field strength E.

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

Outline why the ions are likely to spread out.

Outline why the ions are likely to spread out.

Outline why the ions are likely to spread out.

Outline why the ions are likely to spread out.

Outline why the ions are likely to spread out.

Outline why the ions are likely to spread out.

Two cylinders, X and Y, made from the same material, are connected in series.

The cross-sectional area of Y is twice that of X. The drift speed of the electrons in X is $v_{\text{X}}$ and in Y it is $v_{\text{Y}}$.

What is the ratio $\frac{v_{\text{X}}}{v_{\text{Y}}}$?

A.  4

B.  2

C.  1

D.  $\frac{1}{2}$

Two cylinders, X and Y, made from the same material, are connected in series.

The cross-sectional area of Y is twice that of X. The drift speed of the electrons in X is $v_{\text{X}}$ and in Y it is $v_{\text{Y}}$.

What is the ratio $\frac{v_{\text{X}}}{v_{\text{Y}}}$?

A.  4

B.  2

C.  1

D.  $\frac{1}{2}$

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.

Two copper wires of equal lengths but different diameters are used to connect a cell to a load. Wire 1 has a diameter M, wire 2 has a diameter 2M. The electron drift velocities in wires 1 and 2 are $v_1$ and $v_2$.

What is $\frac{v_2}{v_1}$?

A.  $4$

B.  $2$

C.  $\frac{1}{2}$

D.  $\frac{1}{4}$

Two copper wires of equal lengths but different diameters are used to connect a cell to a load. Wire 1 has a diameter M, wire 2 has a diameter 2M. The electron drift velocities in wires 1 and 2 are $v_1$ and $v_2$.

What is $\frac{v_2}{v_1}$?

A.  $4$

B.  $2$

C.  $\frac{1}{2}$

D.  $\frac{1}{4}$

The electron is replaced by a proton which is also released from rest at X. Compare, without calculation, the motion of the electron with the motion of the proton after release. You may assume that no frictional forces act on the electron or the proton.

The electron is replaced by a proton which is also released from rest at X. Compare, without calculation, the motion of the electron with the motion of the proton after release. You may assume that no frictional forces act on the electron or the proton.

The electron is replaced by a proton which is also released from rest at X. Compare, without calculation, the motion of the electron with the motion of the proton after release. You may assume that no frictional forces act on the electron or the proton.

Calculate the drift speed v of the electrons in the conductor in cm s^–1. State your answer to an appropriate number of significant figures.

Calculate the drift speed v of the electrons in the conductor in cm s^–1. State your answer to an appropriate number of significant figures.

Calculate the drift speed v of the electrons in the conductor in cm s^–1. State your answer to an appropriate number of significant figures.

Calculate the drift speed v of the electrons in the conductor in cm s^–1.

Calculate the drift speed v of the electrons in the conductor in cm s^–1.

Calculate the drift speed v of the electrons in the conductor in cm s^–1.

An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.

An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.

An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.

Calculate, in A, the average current during the discharge.

Calculate, in A, the average current during the discharge.

Calculate, in A, the average current during the discharge.

Show that the speed v of an electron in the hydrogen atom is related to the radius r of the orbit by the expression

$$v=\sqrt{\frac{k{e}^2}{m_{\text{e}}r}}$$

where k is the Coulomb constant.

Show that the speed v of an electron in the hydrogen atom is related to the radius r of the orbit by the expression

$$v=\sqrt{\frac{k{e}^2}{m_{\text{e}}r}}$$

where k is the Coulomb constant.

Show that the speed v of an electron in the hydrogen atom is related to the radius r of the orbit by the expression

$$v=\sqrt{\frac{k{e}^2}{m_{\text{e}}r}}$$

where k is the Coulomb constant.

Two copper wires X and Y are connected in series. The diameter of Y is double that of X. The drift speed in X is v. What is the drift speed in Y?

A.   $\frac{v}{4}$

B.   $\frac{v}{2}$

C.   2v

D.   4v

Two copper wires X and Y are connected in series. The diameter of Y is double that of X. The drift speed in X is v. What is the drift speed in Y?

A.   $\frac{v}{4}$

B.   $\frac{v}{2}$

C.   2v

D.   4v

Two point charges Q₁ and Q₂ are one metre apart. The graph shows the variation of electric potential V with distance $x$ from Q₁.

What is $\frac{Q_1}{Q_2}$?

A.   $\frac{1}{16}$

B.   $\frac{1}{4}$

C.   4

D.   16

Two point charges Q₁ and Q₂ are one metre apart. The graph shows the variation of electric potential V with distance $x$ from Q₁.

What is $\frac{Q_1}{Q_2}$?

A.   $\frac{1}{16}$

B.   $\frac{1}{4}$

C.   4

D.   16

Show that the time taken for the battery to discharge is about 3 × 10³ s.

Show that the time taken for the battery to discharge is about 3 × 10³ s.

Show that the time taken for the battery to discharge is about 3 × 10³ s.

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. $\frac{eV}{n}$

Two parallel plates are a distance apart with a potential difference between them. A point charge moves from the negatively charged plate to the positively charged plate. The charge gains kinetic energy W. The distance between the plates is doubled and the potential difference between them is halved. What is the kinetic energy gained by an identical charge moving between these plates?

A. $\frac{W}{2}$

B. W

C. 2W

D. 4W

Two parallel plates are a distance apart with a potential difference between them. A point charge moves from the negatively charged plate to the positively charged plate. The charge gains kinetic energy W. The distance between the plates is doubled and the potential difference between them is halved. What is the kinetic energy gained by an identical charge moving between these plates?

A. $\frac{W}{2}$

B. W

C. 2W

D. 4W

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 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.

The charge on the ball is 1.2 × 10⁻⁶C. Determine σ.

The charge on the ball is 1.2 × 10⁻⁶C. Determine σ.

The charge on the ball is 1.2 × 10⁻⁶C. Determine σ.

Calculate the charge on Q. State your answer to an appropriate number of significant figures.

Calculate the charge on Q. State your answer to an appropriate number of significant figures.

Calculate the charge on Q. State your answer to an appropriate number of significant figures.

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

The work done to move a particle of charge 0.25 μC from one point in an electric field to another is 4.5 μJ. Calculate the magnitude of the potential difference between the two points.

The work done to move a particle of charge 0.25 μC from one point in an electric field to another is 4.5 μJ. Calculate the magnitude of the potential difference between the two points.

The work done to move a particle of charge 0.25 μC from one point in an electric field to another is 4.5 μJ. Calculate the magnitude of the potential difference between the two points.

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.

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?

Deduce whether the motion of Z is simple harmonic.

Deduce whether the motion of Z is simple harmonic.

Deduce whether the motion of Z is simple harmonic.

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?

Wire $\text{X}$ and wire $\text{Y}$ are connected in series in a circuit. Wire $\text{X}$ has three times the radius and one third the charge carrier density of wire $\text{Y}$.

What is $\frac{\text{drift speed in X}}{\text{drift speed in Y}}$?

A.  $\frac{1}{9}$

B.  $\frac{1}{3}$

C.  $1$

D.  $3$

Wire $\text{X}$ and wire $\text{Y}$ are connected in series in a circuit. Wire $\text{X}$ has three times the radius and one third the charge carrier density of wire $\text{Y}$.

What is $\frac{\text{drift speed in X}}{\text{drift speed in Y}}$?

A.  $\frac{1}{9}$

B.  $\frac{1}{3}$

C.  $1$

D.  $3$

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.  $\frac{Fd}{V}$