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

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?

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.  $\frac{1}{2}$

Outline why the ions are likely to spread out.

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

Outline why the ions are likely to spread out.

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?

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 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

Electrons, each with a charge e, move with speed v along a metal wire. The electric current in the wire is I.

Plane P is perpendicular to the wire. How many electrons pass through plane P in each second?

A.  $\frac{e}{I}$

B.  $\frac{ve}{I}$

C.  $\frac{I}{ve}$

D.  $\frac{I}{e}$

Calculate the magnitude of the initial acceleration of the electron.

Determine the electric field strength E.

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.

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

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

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. State your answer to an appropriate number of significant figures.

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. $\frac{F}{9x^2}$

Calculate the electric potential difference between points A and B.

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

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

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

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

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

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.

Show that the time taken for the battery to discharge is about 3 × 10³ 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.     $\frac{E}{s}$

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.

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.

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

Deduce whether the motion of Z is simple harmonic.