Question

Four identical charges $+50\, \mu C$ each, are placed one at each corner of a square of side $2\, m .$ How much external energy is required to bring another charge of $+50\, \mu C$ from infinity to the centre of the square? $\left(\right.$ Given $\left.\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \frac{ Nm ^{2}}{C^{2}}\right)$

• 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
$W=q\left(V_{0}-V_{\infty}\right)=q V_{0}$
$\Rightarrow W=50 \times 10^{-6} \times 90 \sqrt{2} \times 10^{4}=64\, J$