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Two concentric rings, one of radius R and total charge +Q and the second of radius 2R and total charge -✓8Q, 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?

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$\frac{R}{2}$

$\frac{R}{\sqrt{2}}$

$\frac{R}{2 \sqrt{2}}$

$\sqrt{2} R$

answer is D.

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Detailed Solution

Electric field at a point on z-axis distant r from origin is

$E = \frac{1}{4 {πε}_{0}} (\frac{Qr}{{(r^{2} + R^{2})}^{3 / 2}} - \frac{\sqrt{8} Qr}{{(r^{2} + 4 R^{2})}^{3 / 2}}) = 0 Solving, we get r = \sqrt{2} R$

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