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Q. Potential at any point inside a charged hollow sphere :

UPSEEUPSEE 2005

Solution:

If a charge is taken from one point to another inside a charged spherical shell no work is done.
The electric field inside a spherical charge is zero everywhere.
image
Since, $E=-\frac{d V}{d x} $
$ \therefore \, E=0$,
$\Rightarrow \,\frac{dV}{dx}=0$
image
$\Rightarrow $ V= constant.
The value of potential at spherical shell is given by
$V=\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{k} $ volt
Its value is same as that on the surface.