First slide

Finding field strength using Gauss's Law

Question

The number of electrons to be put on a spherical conductor of radius 0.1 m to produce an electric field of 0.036 N/C just above its surface is

Moderate

A

$2.7 \times 10^{5}$
B

$2.6 \times 10^{5}$
C

$2.5 \times 10^{5}$
D

$2.4 \times 10^{5}$

Solution

$E = \frac{1}{4 {πε}_{0}} \cdot \frac{ne}{r^{2}} \Rightarrow n = \frac{{Er}^{2}}{e} . 4 {πε}_{0} \Rightarrow n = \frac{0.036 \times 0.1 \times 0.1}{9 \times 10^{9} \times 1.6 \times 10^{- 19}} = \frac{360}{144} \times 10^{5} = 2.5 \times 10^{5}$

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