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  4. 4 point charges each +q is placed on the circumference of a circle of diameter 2d in, such a way that they form a square. The potential at the centre is

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Q. $4$ point charges each $+q$ is placed on the circumference of a circle of diameter $2d$ in, such a way that they form a square. The potential at the centre is

WBJEEWBJEE 2008Electrostatic Potential and Capacitance

Solution:

Potential at centre due to all charges are
$=\frac{1}{4 \pi \varepsilon_{0}}\left[\frac{q}{d}+\frac{q}{d}+\frac{q}{d}+\frac{q}{d}\right]$
image
$=\frac{1}{4 \pi \varepsilon_{0}} \frac{4 q}{d}$ in SI units
$=\frac{4 q}{d}$ in CGS units