Question

What is the electric potential at the centre of square of side 1 m? The charges $1\ast {10}^{-8}C,-2\ast {10}^{-8}C,3\ast {10}^{-8}Cand2\ast {10}^{-8}C$ are placed at the corners of the square.

• A. $409V$
• B. $509V$
• C. $600V$
• D. $1018V$

Answer 1

The correct option is C $600V$

Distance of corner from centre of square of side $=1m$

charges $=1\times {10}^{-8}C$ ; $-2\times {10}^{-8}C$

$3\times {10}^{-8}C$ and $2\times {10}^{-8}C$

As shown in the figure all charges are placed at a distance of $1m$ from centre of square. Potential due to $+2\times {10}^{-8}C$ and $-2\times {10}^{-8}C$ and each other hence, net potential is given by

$V=\frac{3q}{4\pi {ϵ}_0}+\frac{q}{4\pi {ϵ}_0}$

$=\frac{4q}{4\pi {ϵ}_0}=\frac{q}{\pi {ϵ}_0}$ where $q=1\times {10}^{-8}$

Hence $V=600V$