Question

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

Answer 1

Answer: (B)

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 $V=\frac{1}{4\pi {\epsilon }_0}\frac{q}{K}volt$ 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 $\left(\propto \frac{1}{r}\right)$ .