The electric potential at the centre of two concentric half rings of radii and , having same linear charge density is

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Solution

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

1 $\frac{2 λ}{ε_{0}}$

2 $\frac{λ}{2 ε_{0}}$

3 $\frac{λ}{4 ε_{0}}$

4 $\frac{λ}{ε_{0}}$

Ans.
(2)

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

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

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

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