Question

A square of side $\sqrt{2}$ has charges of $+2\times {10}^{-9}C,$$1\times {10}^{-9}C,-2\times {10}^{-9}Cand-3\times {10}^{-9}C$ respectively at its corners. The potential at the center of the square is

• A. $-8V$
• B. $+8V$
• C. $-18V$
• D. $+18V$

Answer 1

Answer: (D)

Here the potential due to $2\times {10}^{-9}C$ and $-2\times {10}^{-9}C$ gets cancelled. Hence net potential isgiven by-

$v=\frac{-3q}{4\pi {ϵ}_0}+\frac{q}{4\pi {ϵ}_0}=\frac{-2q}{4\pi {ϵ}_0}=\frac{-q}{2\pi {ϵ}_0}$

where $q={10}^{-9}C$

$v=\left(\frac{-q}{2\pi {ϵ}_0}\right)=+18V$