The electric potential at the centre of a square of side \( \sqrt{2} \) m having charges 90 \( \mu \)C, -60 \( \mu \)C, 30 \( \mu \)C and - 40 \( \mu \)C at the four corners of the square is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 1.8 \times 10^{5}\,\mathrm{V} \)
The centre of a square is at the same distance from all four corners, namely half the diagonal. The potential is a scalar, so the contributions simply add with their signs.
\( \displaystyle r = \frac{\text{diagonal}}{2} = \frac{\sqrt{2}\times\sqrt{2}}{2} = 1\,\mathrm{m} \)
\( \displaystyle V = \frac{k\,(q_1+q_2+q_3+q_4)}{r} = \frac{9\times10^{9}\times(90-60+30-40)\times10^{-6}}{1} \)
\( \displaystyle V = 9\times10^{9}\times20\times10^{-6} = 1.8\times10^{5}\,\mathrm{V} \)