Question

A metallic sphere of radius 2 m is charged in air to a potential of 3000 V. Calculate the energy stored in the sphere.

Answer 1

$\underset{–}{Given:}$

r = radius of sphere = 2m

V = Potential of sphere = 3000V

The energy stored in the sphere will be, U = $\frac{1}{2}$ CV${}^2$

where C $\to$ capacitance of sphere

Thecapacitance of a sphere is,

C = 4$\pi {ϵ}_{0}r$

$=\frac{1}{9\times {10}^9}\times$ 2 = $\frac{2}{9}\times$10${}^{-9}$F

Substituting this value in expression for U, we get,

U = $\frac{1}{2}$CV${}^2$ = $\frac{1}{2}\times \frac{2}{9}\times$(3000)${}^2$10${}^{-9}$

$\Rightarrow$U = 10${}^{-3}$J