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# A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in figure .the electric field inside emptied space isNon zero and uniform Please explain in detail

Arun Kumar IIT Delhi
7 years ago
We will use of superposition theorem here,
Assume whole sphere has charge density
$\rho$
then for smaller sphere to be of zero its charge density should be
$-\rho$
P be a point inside the smaller sphere.
O be centre of the bigger sphere.
S be center of smaller sphere.
We know at P
$\\E_{big\,sphere}=(\rho/3\epsilon)\overrightarrow{OP}\\ E_{small\,sphere}=(-\rho/3\epsilon)\overrightarrow{SP} \\E_{small\,sphere}=(-\rho/3\epsilon)(\overrightarrow{OP}-\overrightarrow{SP})=(\rho/3\epsilon)\overrightarrow{OS}$

Thanks & Regards

Arun Kumar

IIT Delhi

ashu
34 Points
7 years ago
Not able to get how field is uniform inside because above vector shows different directions