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 V/E has magnitude.

Answer 1

Electric field(E)= kQ/r²
Potential (V)= kQ(n-1)/r
Where k= 9*10^9 = constant
Hence,
V/E= (n-1)r

Answer 2

The ratio $\bold{\frac{V}{E}}$ has a value of (n-1) r.

The region around the charged particle that exerts force on other particles or body is Electric field here it is given by $\bold{\mathrm{E}=\frac{k Q}{r^{2}}}$ {the formula is given by coulomb's law}

The charge in electric field is known as Potential and is given by

$\mathrm{V}=\frac{k Q(n-1)}{r}$

Where $k=9 \times 10^{9}$ = constant

Hence, the ratio of potential and electric field is given by

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

Hence, $\frac{V}{E}=(n-1) r$.