Question

A charged sphere of radius $0.02\text{m}$ has charge density of $1{\text{Cm}}^{-2}$. The workdone when a charge of $40\text{nC}$ is moved from infinity to a point that is at a distance of $0.04\text{m}$ from the centre of the sphere.

• A. $1.44\pi \text{J}$
• B. $2\text{J}$
• C. $14.4\pi \text{J}$
• D. $1.44\text{J}$

Answer 1

The correct option is C $14.4\pi \text{J}$

Charge on sphere is
$Q=\sigma S=\sigma \times 4\pi r^2=1\times 4\pi \times (0.02{)}^2$

$=4\pi \times 4\times {10}^{-4}=16\pi \times {10}^{-4}\text{C}$

Workdone $=$ P.E. of the system of two charges

$W=\frac{1}{4\pi {\epsilon }_0}\frac{Qq}{r}$

$=\frac{9\times {10}^9\times 16\pi \times {10}^{-4}\times 40\times {10}^{-9}}{0.04}$

$=9\times 16\pi \times {10}^{-1}$

$=14.4\pi \text{J}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (c) is the correct answer.