Question

Two concentric rings, one of radius $R$ and total charge $+Q$ and the second of radius $2 R$ and total charge $-\sqrt{8} Q$, lie in $x-y$ plane (i.e., $z=0$ plane). The common centre of rings lies at origin and the common axis coincides with $z$ -axis. The charge is uniformly distributed on both the rings. At what distance from origin is the net electric field on $z$ -axis zero?

• A. $\frac{R}{2}$
• B. $\frac{R}{\sqrt{2}}$
• C. $\frac{R}{2 \sqrt{2}}$
• D. $\sqrt{2} R$

Answer 1

Answer: (D)

Electric field at a point on $z$ -axis distant $r$ from origin is $E=\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{Q r}{\left(r^{2}+R^{2}\right)^{3 / 2}}-\frac{\sqrt{8} Q r}{\left(r^{2}+4 R^{2}\right)^{3 / 2}}\right)=0$
Solving, we get $r=\sqrt{2} R$