CAIE A-Level Physics 18.3 Force between Point Charges

Practise applying Coulomb’s law to calculate and interpret force between point charges, rearranging it and reasoning about sign, direction and inverse-square dependence.

Exam points

apply spherical-conductor and Coulomb-law models to calculate and interpret electric force between point charges
rearrange Coulomb relationships and reason about sign, direction and inverse-square dependence

Covered syllabus points

18.3.1—That, for a point outside a spherical conductor, the charge on the sphere 18.3.2—Coulomb’s law F = Q1Q2 / (4πε0 r 2) for the force between two point charges

[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

B1

from x=r to x=3 r : curve with negative gradient of decreasing magnitude passing through ( $r, E_{0}$ )

B1

line passing through ( $2 r, E_{0} / 4$ ) and ( $3 r, E_{0} / 9$ )

B1

[Maximum number: 6]

(a)

State Coulomb's law.

[ 2 ]

(b)

Positronium is a system in which an electron and a positron orbit, with the same period, around their common centre of mass, as shown in Fig. 2.1.

Fig. 2.1 (not to scale)

The radius r of the orbit of both particles is $1.59 \times 10^{-10} \mathrm{~m}$ .

[ 4 ]

(i)

Explain how the electric force between the electron and the positron causes the path of the moving particles to be circular.

[ 2 ]

(ii)

Show that the magnitude of the electric force between the electron and the positron is $2.28 \times 10^{-9} \mathrm{~N}$ .

[ 2 ]

$F=e^{2} / 4 \pi \varepsilon_{0} X^{2}$

C1

$\begin{aligned} =\left(1.60 \times 10^{-19}\right)^{2} /\left[4 \pi \times 8.85 \times 10^{-12} \times\left(2 \times 1.59 \times 10^{-10}\right)^{2}\right] =2.28 \times 10^{-9} \mathrm{~N} \end{aligned}$

A1

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Covered syllabus points

18.3 Electric force between point charges question 1

18.3 Electric force between point charges question 2

Question (a)

Question (b)

Question (i)

Question (ii)