Question

A spherical condenser has inner and outer spheres of radii $a$ and $b$ respectively. The space between the two is filled with air. The difference between the capacities of two condensers formed when outer sphere is earthed and when inner sphere is earthed will be

• A. zero
• B. $4\pi {\epsilon }_{0}a$
• C. $4\pi {\epsilon }_{0}b$
• D. $4\pi {\epsilon }_{0}a\left(\frac{b}{b-a}\right)$

Answer 1

Answer: (C)

Capacity when outer sphere is earthed
$C_1=4\pi {\epsilon }_0\frac{ab}{(b-a)}$
Capacity when inner sphere is earthed
$C_2=4\pi {\epsilon }_{0}b+\frac{4\pi {\epsilon }_{0}ab}{b-a}=4\pi {\epsilon }_0\left(\frac{b^2}{b-a}\right)$
Difference in capacity $=C_2-C_1=4\pi {\epsilon }_{0}b$