The electric potential at the centre of two concentric half rings...

The electric potential at the centre of two concentric half rings of radii ${R}_{1}$ and ${R}_{2}$ , having same linear charge density $\lambda$ is

The electric potential at the centre of two concentric half rings of radii R _ 1 and R _ 2 , having same linear charge .

Options

A $\dfrac{2\lambda}{{\in}_{0}}$
B $\dfrac{\lambda}{2{\in}_{0}}$
C $\dfrac{\lambda}{4{\in}_{0}}$
D $\dfrac{\lambda}{{\in}_{0}}$

Correct answer

B. $\dfrac{\lambda}{2{\in}_{0}}$

Step-by-step solution

The electric potential at the centre of two concentric half rings of radii R _ 1 and R _ 2 , having same linear charge

${V}_{O} = {V}_{1} + {V}_{2}$

$⇒ {V}_{O} = \dfrac{1}{4\pi{ϵ}_{0}} \times \dfrac{{\lambda}_{1}\left(\pi{R}_{1}\right)}{{R}_{1}} + \dfrac{1}{4\pi{ϵ}_{0}} \times \dfrac{{\lambda}_{1}\left(\pi{R}_{2}\right)}{{R}_{2}} = \dfrac{\lambda}{2{ϵ}_{0}}$

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