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Question

A spherical portion has been removed from a solid sphere having a charge distributed
uniformly in its volume as shown in the figure. The electric field inside the emptied
space is :
42470.jpg

A
zero everywhere
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B
non-zero and uniform
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C
non-uniform
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D
zero only at its center
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Solution

The correct option is A non-zero and uniform

If a Gaussian surface is constructed within the cavity then by Gauss Law E.dS=0 . This does not mean that E=0.
From the image, consider a point P inside the cavity and let ρ be the charge density. Then, after applying superposition principle the net electric field at point P will be:
E=ρ3ϵ0bρ3ϵ0a
=ρ3ϵ0r (Since r=ba)
which for a given cavity is independent of the position of a point within the cavity.
Therefore, Electric field is non-zero and uniform within the cavity.


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