First slide

Electric field

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

Easy

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

$E = \frac{1}{4 {πε}_{0}} \cdot \frac{ne}{r^{2}} \Rightarrow n = \frac{{Er}^{2}}{e} \cdot 4 {πε}_{0}$
$\Rightarrow n = \frac{0 .036 \times 0 .1 \times 0 .1}{9 \times 10^{9} \times 1 .6 \times 10^{- 19}} = \frac{360}{144} \times 10^{5} = 2 .5 \times 10^{5} N / C$

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