Two uniformly charged semi circular rings of radius R and linear charge density λ, are placed in y-z and x-z plane as shown. Electric field intensity at point P is λnε0R. Where point P is intersection point of axis of both rings and at distance R from center of both rings. Find value of n.

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Two uniformly charged semi circular rings of radius R and linear charge density $λ,$ are placed in y-z and x-z plane as shown. Electric field intensity at point P is $\frac{λ}{n ε_{0} R} .$ Where point P is intersection point of axis of both rings and at distance R from center of both rings. Find value of n.

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Detailed Solution

At P, the axial component of electric field of both half rings will be at $90 °$ and components to the axis will cancel each other, being at $180 °$
$E_{n e t} = E \sqrt{2}$
Where E is field due to one half ring.
$= [\frac{k λ (π R)}{{(R^{2} + R^{2})}^{3 / 2}} . R] \sqrt{2}$