Question

Two spheres of radius 12cm and16cm have equal charge. The ratio of their energies is

• A. 3:4
• B. 4:3
• C. 2:1
• D. 1:2

Answer 1

The correct option is B 4:3

Energy stored in a capacitor $U=\frac{1}{2}\frac{q^2}{C}$
Capacitance of sphere $=4\pi {ϵ}_{0}r$

$U\propto \frac{1}{C}\Rightarrow U\propto \frac{1}{r}$

$\frac{U_1}{U_2}=\frac{r_2}{r_1}=\frac{16}{12}=\frac{4}{3}\Rightarrow \frac{U_1}{U_2}=\frac{4}{3}$