CAIE A-Level Physics 18.4 Field of a Point Charge

Practise calculating and graphing point-charge electric field strength with E = Q/(4 pi epsilon0 r²), rearranging it and comparing distance effects.

Exam points

calculate and interpret electric field strength due to a point charge using E=Q/(4πε₀r²)
rearrange the point-charge field relationship and compare field strength with distance

Covered syllabus points

18.4.1—E = Q / (4πε0 r 2) for the electric field strength due to a point charge in

[Maximum number: 5]

(a)

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 ]

$g=G M / r^{2}$

M1

$E=Q / 4 \pi \varepsilon_{0} r^{2}$

M1

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

A1

(b)

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.

[ 2 ]

(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 ]

$\begin{aligned} E =\alpha g Q / M =\left(1.35 \times 10^{20} \times 9.81 \times 4.80 \times 10^{5}\right) /\left(5.98 \times 10^{24}\right) \end{aligned}$

C1

$=106 \mathrm{~N} \mathrm{C}^{-1}$ or $106 \mathrm{~V} \mathrm{~m}^{-1}$

A1

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Covered syllabus points

18.4 Electric field of a point charge question 1

Question (a)

Question (i)

Question (b)

Question (i)