A semicircular arc of radius ‘a’ is charged uniformly and the charge per unit length is $λ$ .The electric field at its centre is

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$\frac{λ^{2}}{2 π ε_{o} a}$

$\frac{λ}{2 π ε_{o} a}$

$\frac{λ}{2 π ε_{o} a^{2}}$

$\frac{λ}{4 ε_{o} a}$

answer is D.

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Detailed Solution

$d E = \frac{K λ d x}{a^{2}} d E_{n e t} = \frac{K λ d x}{a^{2}} \cos θ E = \int_{\frac{- π}{2}}^{\frac{π}{2}} \frac{K λ d θ}{a} \cos θ = \frac{λ}{2 π \in_{0} a}$

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