GATE EC 1996 Electromagnetics Solution Q 1

GATE EC 1996 Electromagnetics Solution Q 1

A metal sphere with 1 m radius and a surface charge density of 10 Coulombs/m2 is enclosed in a cube of 10 m side. The total outward electric displacement normal to the surface of the cube is

a) 40\pi\;Coulombs

b) 10\pi\;Coulombs

c) 5\pi\;Coulombs

d) None of the above

Ans- a)

Explanation 

The given charge is completely inside the cube which is a close surface. So according to Gauss’ Theorem,

Where charge enclosed is the charge of the sphere

\begin{array}{l}Q_{enclosed}=\rho_sA=\rho_s\left(4\pi r^2\right)=10\left(4\pi\times1^2\right)\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=40\pi\end{array}

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