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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 $$\oint E.dS=0$$ . This does not mean that $$E = 0$$. 
From the image, consider a point P inside the cavity and let $$\rho$$ be the charge density. Then, after applying superposition principle the net electric field at point P will be: 
$$E=\dfrac{\rho}{3 \epsilon_0}\overrightarrow{b}-\dfrac{\rho}{3\epsilon_0}\overrightarrow{a}$$
$$ =\dfrac{\rho}{3 \epsilon_0}\overrightarrow{r}$$  (Since $$\overrightarrow{r}=\overrightarrow{b}-\overrightarrow{a}$$) 
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. 


571680_42470_ans.JPG

Physics

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