question_answer

    Potential at any point inside a charged hollow, sphere

A)  increases with distance

B)  is a constant

C)  decreases with distance from centre

D)  is zero

Correct Answer: B

Solution :

                Key Idea: 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. Since,          \[E=-\frac{dV}{dx}\] \[\therefore \]  \[E=0,\Rightarrow \frac{dV}{dx}=0\] \[\Rightarrow \]            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. Note: Outside the shell both E and V decrease with distance, E decreases rapidly\[\left( \propto \frac{1}{{{r}^{2}}} \right)\]and decreases compactly slowly\[\left( \propto \frac{1}{r} \right)\].