Question

Four charges ${10}^{-8};-2\times {10}^{-8};+3\times {10}^{-8}$ and $2\times {10}^{-8}$ coulombs are placed at the four corners of a square of side $1m$. The potential at the centre of the square is

• A. $zero$
• B. $360volt$
• C. $180volt$
• D. $360\sqrt{2}$volt

Answer 1

Answer: (D)

$360\sqrt{2}$volt

We know V due to a charge Q $=\frac{kQ}{r}$

Potential at centre $=\frac{k\left({10}^{-8}\right)}{\left(\frac{1}{\sqrt{2}}\right)}+\frac{k(-2\times {10}^{-8})}{\left(\frac{1}{\sqrt{2}}\right)}+\frac{k(2\times {10}^{-8})}{\left(\frac{1}{\sqrt{2}}\right)}$
$+\frac{k(3\times {10}^{-8})}{\left(\frac{1}{\sqrt{2}}\right)}$

$=k\sqrt{2}({10}^{-8}+3\times {10}^{-8})$
$=4\times {10}^{-8}\times 9\times {10}^9\times \sqrt{2}$
$=360\sqrt{2}volts$