Question

Four identical charges $+50\mu C$ each are placed, one at each corner of a square of side 2m. How much external energy is required to bring another charge of $+50\mu C$ from infinity to the centre of the square $(Given\frac{1}{4\pi {ϵ}_0}=9\times {10}^9\frac{N{m}^2}{C^2})$

• A. 64 J
• B. 41 J
• C. 16 J
• D. 10 J

Answer 1

The correct option is A 64 J

Potential at the centre of square
$V=4\times \left(\frac{9\times {10}^9\times 50\times {10}^{-6}}{\sqrt{2}}\right)=90\sqrt{2}\times {10}^{4}V$
Work done in bringing a charge (q = $50\mu C$) from $\infty$ to centre (O) of the square is
$W=q(V_0-V_{\infty })=q{V}_0$
$\Rightarrow W=50\times {10}^{-6}\times 90\sqrt{2}\times {10}^4=64J$