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 $\frac{1}{4\pi {\epsilon }_0}=9\times 10^9\frac{N{m}^2}{C^2})$

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

Answer 1

Answer: (A)

Potential at the centre of square
$V_0=4\times {\left(\frac{9\times 10^9\times 50\times 10^{-6}}{2/\sqrt{2}}\right)}^0$
$=90\sqrt{2}\times 10^{4}V$
Work done in bringing a charge $(q=50\mu C)$
from $\infty$ to centre $(O)$ of the square is
$W=q\left(V_0-V_{\infty }\right)=q{V}_0$
$\Rightarrow W=50\times 10^{-6}\times 90\sqrt{2}\times 10^4=64J$