Question

A thin spherical shell of radius 20 cm is uniformly charged with Q.$V_0$ the potential on it's surface. Another point charge Q is now placed at the centre of the shell. V be the net potential (new) potential at a point 15 cm from it's centre then, V equals to:

• A. 3/2 $V_0$
• B. 5/3 $V_0$
• C. 4/3 $V_0$
• D. 9/4 $V_0$

Answer 1

The correct option is C 4/3 $V_0$

Radius $=20cm$ $=20\times {10}^{-2}m$

charge $=Q$

$V_0=$ potential

net potential $=V$

$V_0=\frac{1}{4\pi {ϵ}_0}\frac{Q}{20\times {10}^{-2}}$ or, $V_0\times 20\times {10}^{-2}=\frac{Q}{4\pi {ϵ}_0}$

$V^1=\frac{1}{4\pi {ϵ}_0}\frac{Q}{15\times {10}^{-2}}$

$V^1=\frac{1}{4\pi {ϵ}_0}\frac{Q}{15\times {10}^{-2}}=\frac{20\times {10}^{-2}\times V_0}{15\times {10}^{-2}}=\frac{4}{3}{V}_0$