Question

Four electric charges $+q$ , $+q$ , $-q$ and $-q$ are placed at the corners of a square of side $2L$ ( see figure ). The electric potential at point $A$ , midway between the two charges $+q$ and $+q$ , is

• A. $\frac{12q}{4\pi {\epsilon }_{0}L}(1+\sqrt{5})$
• B. $\frac{1}{4\pi {\epsilon }_0}\frac{2q}{L}\left(1+\frac{1}{\sqrt{5}}\right)$
• C. zero
• D. $\frac{12q}{4\pi {\epsilon }_{0}L}\left(1-\frac{1}{\sqrt{5}}\right)$

Answer 1

Answer: (D)

Distance of point A from the two +q charges = L.
Distance of point A from the two -q charges = $\sqrt{{\mathrm{L}}^2+(2\mathrm{L}{)}^2}$=$\sqrt{5L}$

$\therefore$ ${\left(\text{V}\right)}_{\text{A}}=\left(\frac{\text{Kq}}{\text{L}}\times 2\right)-\left(\frac{\text{Kq}}{\sqrt{5}\text{L}}\times 2\right)$
$=\frac{2\text{Kq}}{\text{L}}[1-\frac{1}{\sqrt{5}}]$
$=\frac{1}{4\pi {\left(\in \right)}_0}\cdot \frac{2\text{q}}{\text{L}}\left(1-\frac{1}{\sqrt{5}}\right)$