Question

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

• A. $rn$
• B. $r (n-1)$
• C. $(n-1)/r$
• D. $r(n-1) /n$

Answer 1

Answer: (B)

$r (n-1)$

Answer 2

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, $\frac{V}{E}=\frac{k\left(n-1\right)Q}{r}\times\frac{r^{2}}{KQ}$ $=\left(n-1\right)r$