Question

There is a uniformly charged non conducting solid sphere made of material of dielectric cons†an t one. If electric potential at infinity be zero, then the potential at its surface is V. If we take electric potential at its surface to be zero, then the potential at the centre will be

Answer 1

Electric potential inside a uniformly charged solid sphere at a point inside it at a distance r

from its centre is given by, $V=\frac{KQ}{2R^3}(3R^2-r^2)$

if potentia I at infinity is taken to be zero. W here R is radius of solid sphere

For centre of sphere r = 0

$V_c=\frac{KQ}{2R^3}\left(3R^2\right)=\frac{3KQ}{2R}$

F or a point at surfa ce of sphere

r = R

$V_S=\frac{KQ}{2R^3}(3R^2-R^2)=\frac{KQ}{R}$

$V_c-V_S=\frac{3KQ}{2R}-\frac{KQ}{R}=\frac{KQ}{R}=\frac{V}{2}$

Now if reference point corresponding to zero potential is changed and V surface = 0

${V^{\prime }}_S=V_S+U_o$

$0=V+U_o$

$-V=U_o$

$V_C^{\prime }=V_C+U_o$

$V_c^{\prime }=V_C-V$

$V_c^{\prime }=\frac{3KQ}{2R}-V=\frac{3}{2}V-V=\frac{V}{2}$