A hollow metal sphere of radius $R$ is charged with a charge $Q .$ The electric potential and intensity inside the sphere are respectively

• A

  $\frac{Q}{4 \pi \varepsilon_{0} R^{2}}$ and $\frac{Q}{4 \pi \varepsilon_{0} R}$
• Correct answer
  B

  $\frac{Q}{4 \pi \varepsilon_{0} R}$ and zero
• C

  zero and zero
• D

  $\frac{4 \pi \varepsilon_{0} Q}{R}$ and $\frac{Q}{4 \pi \varepsilon_{0} R^{2}}$

Solution

Inside a hollow charged sphere, the electric field intensity is always zero. $\therefore$ $E=0$ but potential is constant. Potential on the surtace of the hollow sphere $$ V=\frac{K Q}{R}=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q}{R}=\frac{Q}{4 \pi \varepsilon_{0} R} $$ This is the potential $(\mathrm{V})$ inside the charged hollow meta sphere.

Hence, the correct answer is option: 'B'.