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. $V =\frac{10 q }{4 \pi \epsilon_{0} R } ; E =\frac{10 q }{4 \pi \in_{0} R ^{2}}$
• B. $V =0, E =\frac{10 q }{4 \pi \epsilon_{0} R ^{2}}$
• C. $V =0, F =0$
• D. $V =\frac{10 q }{4 \pi \epsilon_{0} R } ; E =0$

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.