Question

A hollow sphere of radius $2R$ is charged to $V$ volts and another smaller sphere of radius $R$ is placed inside the bigger sphere without changing the net charge on each sphere. The potential difference between the two spheres would be :

• A. $\frac{3V}{2}$
• B. $\frac{V}{4}$
• C. $\frac{V}{2}$
• D. $V$

Answer 1

Answer: (B)

$\frac{V}{4}$
$Given:$ A hollow sphere of radius 2R ; smaller sphere of radius

$Solution:$ Charge on smaller sphere

$q=C\left(\frac{V}{2}\right)$

$=\frac{4\pi {\epsilon }_{0}RV}{2}$

Potential difference $=\frac{q}{4\pi {\epsilon }_0}(\frac{1}{R}-\frac{1}{2R})$

$=\left(\frac{VR}{2}\right)\left(\frac{1}{2R}\right)=\frac{V}{4}$

$So,the$ $correct$ $option:B$