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  4. In a regular polygon of n sides, each corner is at a distance r from the centre. Identical charges are placed at (n - 1) corners. At the centre, the magnitude of intensity is E and the potential is V. The ratio V/E is

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Q. In a regular polygon of $n$ sides, each corner is at a distance $r$ from the centre. Identical charges are placed at $(n - 1)$ corners. At the centre, the magnitude of intensity is $E$ and the potential is $V$. The ratio $V/E$ is

Electrostatic Potential and Capacitance

Solution:

At the centre, the intensity is effectively due to one charge and the potential is due to $(n - 1)$ charges
$\therefore E=\frac{KQ}{r^{2}}$ and $V=\frac{k\left(n-1\right)Q}{r}$
Hence, $\frac{V}{E}=\frac{k\left(n-1\right)Q}{r}\times\frac{r^{2}}{KQ}$
$=\left(n-1\right)r$