The electric potential at the centre of two concentric half rings of radii R₁ and R₂, having same linear charge density ' λ ' is ( ε₀ = permittivity of free space) (a) (2λ)/(ε₀) (b) (λ)/(2ε₀) (c) (λ)/(4ε₀) (d) (λ)/(ε₀)

Answer: (b). Half ring: V = (k(λπ R))/(R) = (λ)/(4ε₀), independent of R. Both rings have the same λ; potentials add as scalars. V = 2×(λ)/(4ε₀) = (λ)/(2ε₀) So the answer is (b).

The electric potential at the centre of two concentric half rings of… | MHT CET 2024 (4 May, Shift 1)

Q51MHT CET 2024 · 4 MAY · SHIFT 1Medium

Electric Potential & Equipotentials

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 ( $\varepsilon_0 =$ permittivity of free space)

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Answer: (b)

Half ring: $V = \dfrac{k(\lambda\pi R)}{R} = \dfrac{\lambda}{4\varepsilon_0}$ , independent of $R$ .
Both rings have the same $\lambda$ ; potentials add as scalars.
$V = 2\times\dfrac{\lambda}{4\varepsilon_0} = \dfrac{\lambda}{2\varepsilon_0}$
So the answer is (b).

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