Question 194 of 311

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$V=\dfrac{10q}{4\pi {ϵ}_{0}R};E=0$B$V=0,E=\dfrac{10q}{4\pi {ϵ}_{0}{R}^{2}}$C$V=0;E=0$D$V=\dfrac{10q}{4\pi {ϵ}_{0}R};E=\dfrac{10q}{4\pi {ϵ}_{0}{R}^{2}}$

Show answer and solution▾

Answer: (C) $V=0;E=0$

${v}_{net}=5\left(\dfrac{kq}{R}\right)+\left(\dfrac{5k(-q)}{R}\right)$
${v}_{net}=0,\left[{Q}_{net}=0\right]$
${E}_{net}=0$, by symmetry