Physics - Electrostatics Question with Solution | TestHub

Let the corners of the square be A, B, C, and D in order, with charges $+q$, $+q$, $-q$, and $-q$ respectively.

The side length of the square is $2r$.

Let P be the midpoint of the side CD, which connects the two negative charges.

The distance of P from the charges at C and D is:

$r_C=r_D=r$

The distance of P from the charges at A and B can be found using the Pythagorean theorem:

$r_A=r_B=\sqrt{r^2+(2r{)}^2}=\sqrt{5}r$

The total electric potential at P is the algebraic sum of the potentials due to all four charges:

$V=V_A+V_B+V_C+V_D$

$V=\frac{1}{4\pi {ϵ}_0}\left(\frac{q}{\sqrt{5}r}+\frac{q}{\sqrt{5}r}-\frac{q}{r}-\frac{q}{r}\right)$

$V=\frac{1}{4\pi {ϵ}_0}\left(\frac{2q}{\sqrt{5}r}-\frac{2q}{r}\right)$

$V=\frac{1}{4\pi {ϵ}_0}\frac{2q}{r}\left[\frac{1}{\sqrt{5}}-1\right]$

Answer: $\frac{1}{4\pi {ϵ}_0}\frac{2q}{r}\left[\frac{1}{\sqrt{5}}-1\right]$