First slide

Electrostatic potential energy

Question

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

Easy

A

64 J
B

41 J
C

16 J
D

10 J

Solution

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

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