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 intensity is E and the potential is V. The ratio $\frac{V}{E}$ has magnitude.

• A. $rn$
• B. $r(n-1)$
• C. $\frac{(n-1)}{r}$
• D. $\frac{r(n-1)}{n}$

Answer 1

The correct option is B $r(n-1)$

Electric field will be towards the missing change position and will have magnitude equal to thefield due to the missing charge.
$E=\frac{1}{4\pi {ϵ}_0}\frac{q}{r^2}$
Since potential is a scalar
$V=\frac{1}{4\pi {ϵ}_0}\frac{(n-1)q}{r}$
$\Rightarrow \frac{V}{E}=r(n-1)$