First slide

Gauss's Law

Question

A point charge $+ 12 μ C$ is placed at the centre of a thin charged metallic shell of radius 10 cm. It charge on the shell is $- 2 μ C$ , intensity of electric field at a distance 30 cm from the centre of the shell is

Moderate

A

$10^{5} N / C$
B

$10^{4} N / C$
C

$10^{3} N / C$
D

$10^{6} N / C$

Solution

Consider a spherical Gaussian surface of radius 30 cm with its centre at the location of $+ 9 μ c$ charge
$∴ Q_{n e t} = (12 - 2) μ C = 10 μ C$
By Gauss's law, $Q_{n e t} = \in_{0} . ϕ_{E} \Rightarrow Q_{n e t} = \in_{0} . E .4 π r^{2}$
$∴ E = \frac{1}{4 π \in_{0}} \frac{Q_{n e t}}{r^{2}} = 9 \times 10^{9} \times 10 \times 10^{- 6} / {(0.3)}^{2} \frac{N}{C} = 10^{6} \frac{N}{C}$

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