Question

Charges 5 u C, -2 u C, 3 u C and -9 u C are
placed at the corners A, B,C and D of a square ABCD
of side 1m. The net electric potential at the centre of
the square is
1) -27 KV 2) -27root 2 KV
3) - 90KV 4) zero​

Answer 1

Answer:

$- 27 \sqrt{2} kv$

$v = \frac{k \times q}{r} \\ (q \: put \: with \: sign) \\ distance \: from \: corner \: to \: center \\ r = \frac{1 \times \sqrt{2} }{2} = \frac{1}{ \sqrt{2} } \\ v = \frac{k \times 5 \times {10}^{ - 6} }{ \frac{1}{ \sqrt{2} } } + \frac{k \times ( - 2 \times {10}^{ - 6} )}{ \frac{1}{ \sqrt{2} } } + \frac{k \times 3 \times {10}^{ - 6} }{ \frac{1}{ \sqrt{2} } } + \frac{k \times ( - 9 \times {10}^{ - 6} }{ \frac{1}{ \sqrt{2} } } \\ v = \frac{9 \times {10}^{9} \times {10}^{ - 6} }{ \frac{1}{ \sqrt{2} } } (5 - 2 + 3 - 9) \\ v = 9 \times \sqrt{2} \times {10}^{3} \times ( - 3) \\ v = - 27 \sqrt{2} \times {10}^{3} \\ v = - 27 \sqrt{2} kv$