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Question

Electric field in a certain region is acting radially outward and variation of electric field with distance from origin of field is represented below. Slope of the straight line given in the graph is A.


The charge contained in a sphere of radius a centred at the origin of field will be given by

A
πεoAa3
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B
4πεoAa3
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C
4πεoAa2
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D
πεoAa2
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Solution

The correct option is B 4πεoAa3
Slope of the straight line passing through origin is A. Thus equation relating E and r will be

E=Ar ....(1)

Let us consider a gaussian sphere of radius a centered origin of field.

Since E is radially outwards, applying Gaussian law,

ϕ=E.dA=EA=qinεo

EA=qinεo

Substituting the values, we get

Ar×(4×πr2)=qinεo

For the surface r=a,

Aa×(4×πa2)=qinεo

qin=4πεoAa3

Hence, the correct option is (b).

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