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Q.

The electric potential at the centre of two concentric half rings of radii $R_{1}$ and $R_{2}$ having same linear charge density $λ$ is :

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a

$\frac{λ}{ϵ_{0}}$

b

$\frac{λ}{4 \in_{0}}$

c

$\frac{2 λ}{ϵ_{0}}$

d

$\frac{λ}{2 ϵ_{0}}$

answer is D.

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Detailed Solution

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The potential at the center is sum of the potentials due to ring 1 and ring 2.

$V = V_{1} + V_{2}$

$\Rightarrow V = \frac{k [λ ({πR}_{1})]}{R_{1}} + \frac{k [λ ({πR}_{2})]}{R_{2}} = \frac{λ}{2 \in_{0}}$

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The electric potential at the centre of two concentric half rings of radii R1 and R2 having same linear charge density λ is :