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Question

Electric field at center O of semicircle of radius a having linear charge density λ is given as :
71100_b79ccc66804b48038e439455a5fc4884.png
  1. 2λϵoa
  2. λπϵoa
  3. λ2πϵoa
  4. λπϵoa

A
2λϵoa
B
λ2πϵoa
C
λπϵoa
D
λπϵoa
Solution
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Consider an element having charge dq at angle θ of angular width dθ
Length of element =adθ
dq=λadθ
Field due to this element =dE=dq4πϵ0a2
dE=λadθ4πϵ0a2=λdθ4πϵ0a

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