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Electric Field of a Finite Line Charge

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A finite line of charge with length 2L2L and uniform linear charge density λ\lambda is positioned on the x-axis from x=−Lx = -L to x=Lx = L. What is the magnitude of the electric field at point P, located at coordinates (0,d)(0, d) where d>0d > 0?

A

(kλ/d)tan⁡−1(L/d)(k\lambda/d)\tan^{-1}(L/d)

B

(2kλ/d)sin⁡−1(L/L2+d2)(2k\lambda/d)\sin^{-1}(L/\sqrt{L^2 + d^2})

C

(2kλL)/(dL2+d2)(2k\lambda L)/(d\sqrt{L^2 + d^2})

D

(2kλ/d)tan⁡−1(L/d)(2k\lambda/d)\tan^{-1}(L/d)

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