question_answer

A point charge q is placed inside a conducting spherical shell of inner radius 2R and outer radius 3R at a distance of R from centre of the shell. The electric potential at the centre of shell will be.

A) \[\frac{q}{4\pi {{\in }_{0}}2R}\]

B) \[\frac{4q}{12\pi {{\in }_{0}}R}\]

C) \[\frac{5q}{24\pi {{\in }_{0}}R}\]

D)  Can't be determined

Correct Answer: B

Solution :

Due to induction - q charge will come at the inner surface of shell and +q will come on outer surface of shell

Now

\[{{V}_{at0}}={{V}_{due\,\,to\,\,q}}+{{V}_{due\,to-q\,on\,inner\,surface}}+{{V}_{due\,to+q\,on\,outer\,surface}}\]

at \[0=\frac{kq}{R}+\frac{k\,(-\,q)}{2R}+\frac{kq}{3R}=\left( k=\frac{6q-3q+2q}{6R} \right)\]

\[=\frac{5q}{24\pi {{\in }_{0}}R}\,\,\,\,\,\,\,\,\left( k=\frac{1}{4\pi {{\in }_{0}}} \right)\]