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. $\frac{1}{ 4 \pi \varepsilon_0 } \frac{ 2q}{ L} (1 + \sqrt 5)$
• B. $\frac{1}{ 4 \pi \varepsilon_0 } \frac{ 2q}{ L} \bigg [ 1 - \frac{ 1}{ \sqrt 5} \bigg ]$
• C. $\frac{1}{ 4 \pi \varepsilon_0 } \bigg(1 + \frac{ 2q}{ L} (1 - \frac{1}{\sqrt 5})\bigg)$
• D. zero

Answer 1

Answer: (C)

$\frac{1}{ 4 \pi \varepsilon_0 } \bigg(1 + \frac{ 2q}{ L} (1 - \frac{1}{\sqrt 5})\bigg)$

Answer 2

$V _{ A }=\frac{ kq }{ L }+\frac{ kq }{ L }-\frac{ kq }{\sqrt{5}\, L }-\frac{ kq }{\sqrt{5}\, L }$
$=\frac{2 \,kq }{ L }\left(1-\frac{1}{\sqrt{5}}\right)$