Question

In a region of uniform electric field of magnitude $10\text{N/C}$, what will be the energy stored in a sphere of radius $3\text{m}?$

• A. $5\times {10}^{-8}\text{J}$
• B. $9\times {10}^{-8}\text{J}$
• C. $4\times {10}^{-8}\text{J}$
• D. $2\times {10}^{-8}\text{J}$

Answer 1

The correct option is A $5\times {10}^{-8}\text{J}$

We know that electrical energy density is given by :
$E.D=\frac{1}{2}{ϵ}_o{E}^2$

Therefore, energy inside the given sphere will be :
$\text{Energy}=\frac{1}{2}{ϵ}_o{E}^2\times 4\pi R^2$

$\text{Energy}=\frac{1}{2}\times 4\pi {ϵ}_o\times {10}^2\times 3^2$

$\text{Energy}=\frac{1}{2}\times \frac{1}{9\times {10}^9}\times {10}^2\times 9$

$\text{Energy}=5\times {10}^{-8}\text{J}$