There are three conecentric hollow spheres of radii a, b and c and they are charged with charges `q_(1),q_(2)` and `q_(3)` respectively. Calculate the potential of the spheres.

Explanation

Let `V_(1) and V_(2)` be the net potentials of innermost and outermost spherical shells.

Potential due to the hollow sphere at points outside or on its surface is same as that of a point charge if it is placed at its centre. But for points inside the shell, potential is same everywhere and is equal to its value on the surface.
`V_(1)=(1)/(4pi epsilon_(0)) (q_(1))/(a)+(1)/(4pi epsilon_(0)) (q_(2))/(b) +(1)/(4pi epsilon_(0)) (q_(3))/(c )`
`V_(2)=(1)/(4piepsilon_(0))(q_(1))/(c )+(1)/(4pi epsilon_(0)) (q_(2))/(c )+(1)/(4pi epsilon_(0))(q_(3))/(c )`
`V_(1)-V_(2)=((1)/(4pi epsilon_(0)) (q_(1))/(a)+(1)/(4pi epsilon_(0)) (q_(2))/(b) +(1)/(4pi epsilon_(0)) (q_(3))/(c )) - ((1)/(4pi epsilon_(0))(q_(1))/(c )+(1)/(4pi epsilon_(0)) (q_(2))/(c ) +(1)/(4pi epsilon_(0)) (q_(3))/(c ))`
`rArr V_(1)-V_(2)=(q_(1))/(4pi epsilon_(0)) ((1)/(a)-(1)/(c )) +(q_(2))/(4pi epsilon_(0)) ((1)/(b)-(1)/(c ))`