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

Answer 1

The correct option is C $V=0;E=0$

Potential at the centre, $V_c=\frac{K{Q}_{net}}{R}$

$\because Q_{net}=0$

$\therefore V_c=0$

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.