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(B) The electric potential is a scalar quantity. The potential at the center is the sum of the potentials due to $(n - 1)$ charges,each of magnitude $

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$r(n - 1)$

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(B) The electric potential is a scalar quantity. The potential at the center is the sum of the potentials due to $(n - 1)$ charges,each of magnitude $q$.$V = (n - 1) 	imes \frac{kq}{r} = \frac{k(n - 1)q}{r}$The electric field is a vector quantity. In a regular polygon with $n$ corners,if charges were placed at all $n$ corners,the net electric field at the center would be zero due to symmetry.Let the missing charge be at the $n^{th}$ corner. The field due to the $(n - 1)$ charges is equal and opposite to the field that would be produced by a single charge $q$ at the $n^{th}$ corner.Thus,the magnitude of the electric field at the center is $E = \frac{kq}{r^2}$.Calculating the ratio $V/E$:$\frac{V}{E} = \frac{k(n - 1)q}{r} 	imes \frac{r^2}{kq} = r(n - 1)$.

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.

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