Question

Two spheres of radii $12$ cm and $16$ cm have equal charge. The ratio of their energies is :

• A. 3 : 4
• B. 4 : 3
• C. 1 : 2
• D. 2 : 1

Answer 1

The correct option is B 4 : 3

The capacitance of a spherical capacitor is,
$4\pi {ϵ}_{0}rR/(R-r)$
When $R\to \infty$ , capacitance $\to 4\pi {ϵ}_{0}r$
Also energy $=Q^2/2C\Rightarrow E\propto 1/r$
Thus,
$E_1/E_2=r_2/r_1=16/12=4/3$