CAIE A-Level Physics A2 18 Electric Fields Questions

Practise analysing electric fields, force and potential, including field lines, uniform plates, Coulomb’s law, gradients and point-charge energy.

Exam points

represent electric fields and field lines and calculate force or field strength
analyse uniform fields and charged-particle motion between plates
apply Coulomb’s law and point-charge field relationships
calculate electric potential, potential gradient and point-charge potential energy

Covered syllabus points

18.1 Electric fields and field lines 18.2 Uniform electric fields 18.3 Electric force between point charges 18.4 Electric field of a point charge 18.5 Electric potential

[Maximum number: 8]

(a)

Define electric field.

[ 2 ]

(b)

Fig. 5.1 shows two parallel conducting plates that are in a vacuum. The plates are separated by a distance of 6.7 cm and have a potential difference (p.d.) of 430 V between them.

Fig. 5.1

[ 6 ]

(i)

On Fig. 5.1, draw four field lines to represent the electric field between the plates.

[ 2 ]

(ii)

Determine the strength E of the electric field between the plates.

E=\ldots \ldots \ldots \ldots \ldots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ \mathrm{NC}^{-1}

[ 2 ]

E=V / d
E=430 / 0.067
$=6.4 \times 10^{3} \mathrm{~N} \mathrm{C}^{-1}$

(iii)

An electron travels at a speed of $2.6 \times 10^{7} \mathrm{~ms}^{-1}$ towards the region between the plates, as shown in Fig. 5.1.

On Fig. 5.1, draw the path of the electron as it moves between and beyond the plates.

[ 2 ]

[Maximum number: 12]

(a)

State what is indicated by the direction of an electric field line.

[ 2 ]

(b)

Fig. 4.1 shows a pair of parallel metal plates with a potential difference (p.d.) of 2400 V between them.

Fig. 4.1

The plates are separated by a distance of 4.6 cm . The plates are in a vacuum.

[ 5 ]

(i)

On Fig. 4.1, draw five lines to represent the electric field in the region between the plates.

[ 3 ]

(ii)

Calculate the strength of the electric field between the plates.
electric field strength = $\mathrm{NC}^{-1}$

[ 2 ]

E=V / d
$\text { = } 2400 \text { / } 0.046$ $=5.2 \times 10^{4} \mathrm{~N} \mathrm{C}^{-1}$

(c)

A moving proton enters the region between the plates from the left, as shown in Fig. 4.2.

Fig. 4.2

[ 5 ]

(i)

The proton is deflected by the electric field.

On Fig. 4.2, draw a line to show the path of the proton as it moves through and out of the region of the electric field.

[ 2 ]

(ii)

A helium nucleus $\left({ }_{2}^{4} \mathrm{He}\right)$ now enters the region of the electric field along the same initial path as the proton and travelling at the same initial speed.

State and explain how the final speed of the helium nucleus compares with the final speed of the proton after leaving the region of the electric field.

[ 3 ]

[Maximum number: 3]

An isolated metal sphere of radius r is charged so that the electric field strength at its surface is $E_{0}$ .

On Fig. 6.1, sketch the variation of the electric field strength E with distance x from the centre of the sphere. Your sketch should extend from x=0 to x=3 r.

Fig. 6.1

from x=0 to x=r: E=0
from x=r to x=3 r : curve with negative gradient of decreasing magnitude passing through ( $r, E_{0}$ )
line passing through ( $2 r, E_{0} / 4$ ) and ( $3 r, E_{0} / 9$ )

[Maximum number: 7]

(a)

Define electric field.

[ 1 ]

(b)

An isolated uniform conducting sphere has mass M and charge Q.

The gravitational field strength at the surface of the sphere is g.
The electric field strength at the surface of the sphere is E.

[ 3 ]

(i)

Show that

\frac{M}{Q}=\alpha \frac{g}{E}

where $\alpha$ is a constant.

[ 3 ]

$g=G M / r^{2}$ $E=Q / 4 \pi \varepsilon_{0} r^{2}$
algebra showing the elimination of r leading to $M / Q=\left(1 / 4 \pi G \varepsilon_{0}\right)(g / E)$

(c)

Assume that the Earth is a uniform conducting sphere of mass $5.98 \times 10^{24} \mathrm{~kg}$ . The surface of the Earth carries a charge of $-4.80 \times 10^{5} \mathrm{C}$ that is evenly distributed.

[ 3 ]

(i)

Use the information in (b) to determine the electric field strength at the surface of the Earth. Give a unit with your answer.
electric field strength = unit

[ 2 ]

$\begin{aligned} E =\alpha g Q / M =\left(1.35 \times 10^{20} \times 9.81 \times 4.80 \times 10^{5}\right) /\left(5.98 \times 10^{24}\right) \end{aligned}$ $=106 \mathrm{~N} \mathrm{C}^{-1}$ or $106 \mathrm{~V} \mathrm{~m}^{-1}$

(ii)

State how the direction of the electric field at the surface of the Earth compares with the direction of the gravitational field.

[ 1 ]

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Covered syllabus points

Question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question 2

Question (a)

Question (b)

Question (i)

Question (ii)

Question (c)

Question (i)

Question (ii)

Question 3

Question 4

Question (a)

Question (b)

Question (i)

Question (c)

Question (i)

Question (ii)