Question

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 $(+q)$ each, while $2,4,6,8,10$ have charge $(-q)$ each. The potential $V$ and the electric field $E$ at the centre of the circle are respectively: (Take $V=0$ at infinity)

• A. $V=\frac{10q}{4\pi {ϵ}_{0}R};E=\frac{10q}{4\pi {\in }_0{R}^2}$
• B. $V=0,E=\frac{10q}{4\pi {ϵ}_0{R}^2}$
• C. $V=0,F=0$
• D. $V=\frac{10q}{4\pi {ϵ}_{0}R};E=0$

Answer 1

Answer: (C)

Potential of centre $=V=\Sigma \left(\frac{kq}{R}\right)$
$V_C=\frac{K(\Sigma q)}{R}$

$V_C=\frac{K(0)}{R}=0$
Electric field at centre ${\vec{E}}_B=\Sigma \vec{E}$
Let $E$ be electric field produced by each charge at the centre, then resultant electric field will be

$E_C=0$, Since equal electric field vectors are acting at equal angle so their resultant is equal to zero.