Ten charges are placed on the circumference of a circle of radius $R$ with constant angular separation between successive charges.
Alternate charges $1,3,5,7,9$ have charge $(+\mathrm{q})$ each, while $2,4,6,8,10$ have charge $(-q)$ each. The potential $\mathrm{V}$ and the electric field $\mathrm{E}$ at the centre of the circle are respectively:
(Take $\mathrm{V}=0$ at infinity)
Correct Option: , 3
Potential of centre $=\mathrm{V}=$
$\Sigma\left(\frac{\mathrm{kq}}{\mathrm{R}}\right)$
$\mathrm{V}_{\mathrm{C}}=\frac{\mathrm{K}(\Sigma \mathrm{q})}{\mathrm{R}}$
$\mathrm{V}_{\mathrm{C}}=\frac{\mathrm{K}(0)}{\mathrm{R}}=0$
Electric field at centre $\overrightarrow{\mathrm{E}}_{\mathrm{B}}=\Sigma \overrightarrow{\mathrm{E}}$
Let $\mathrm{E}$ be electric field produced by each charge at the centre, then resultant electric field will be
$\mathrm{E}_{\mathrm{C}}=0$, Since equal electric field vectors are acting at equal angle so their resultant is equal to zero.