A uniformly charged half ring of a radius ' R ' has linear charge density ' σ '. The electric potential at the centre of the half ring is ( ε₀ = permittivity of free space) (a) (σ)/(6ε₀) (b) (σ)/(2ε₀) (c) (σ)/(ε₀) (d) (σ)/(4ε₀)

Answer: (d). Charge on half ring q = σπ R, all at distance R from the centre. V = (σπ R)/(4πε₀ R) = (σ)/(4ε₀) So the answer is (d).

A uniformly charged half ring of a radius ' R ' has linear charge… | MHT CET 2021 (20 Sep, Shift 1)

Q80MHT CET 2021 · 20 SEP · SHIFT 1Medium

Electric Potential & Equipotentials

A uniformly charged half ring of a radius ' $R$ ' has linear charge density ' $\sigma$ '. The electric potential at the centre of the half ring is ( $\epsilon_0 =$ permittivity of free space)

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Answer: (d)

Charge on half ring $q = \sigma\pi R$ , all at distance $R$ from the centre.
$V = \dfrac{\sigma\pi R}{4\pi\epsilon_0 R} = \dfrac{\sigma}{4\epsilon_0}$
So the answer is (d).

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