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 $\frac{λ}{k ε_{0}}$ . Then the value of $k$ is.

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answer is 2.

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Detailed Solution

$d v = \frac{1}{4 π \in_{0}} \frac{λ d l}{R}; v = \int d v = \frac{1}{4 π \in_{0}} \frac{λ l}{R}$

Potential at centre, $V = V_{2} + V_{1}$

$\Rightarrow V = \frac{(λ . π R_{2})}{4 π ε_{0} R_{2}} + \frac{(λ . π R_{1})}{4 π ε_{0} R_{1}} = \frac{λ}{2 ε_{0}}$

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