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

$\left( \text{Given}\frac{1}{4\pi\varepsilon_{0}} = 9 \times 10^{9}\frac{Nm^{2}}{C^{2}} \right)$

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

Answer 1

Answer: (A)

$64J$

Answer 2

Potential at the centre of square

$V = 4 \times \left( \frac{9 \times 10^{9} \times 50 \times 10^{- 6}}{2/\sqrt{2}} \right) = 90\sqrt{2} \times 10^{4}V$

Work done in bringing a charge (q = 50 μC) from ∞ to centre (O) of the square is

$W = q(V_{0} - V_{\infty}) = qV_{0}$

⇒ $W = 50 \times 10^{- 6} \times 90\sqrt{2} \times 10^{4} = 64J$