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Question

A thin semi-circular ring of radius ‘r’ has a positive charge ‘q’ distributed uniformly over it. The net electric field at the centre O is

  1. q4π2ϵ0r2^j
  2. q2π2ϵ0r2^j
  3. q4π2ϵ0r2^j
  4. q2π2ϵ0r2^j


Solution

The correct option is D q2π2ϵ0r2^j
The electric field can be written as,
E=dE sin θ         qπr
                                                 dqdr
=Kdqr2sinθ       qπr=dqdrdq=qπrdr
=Kr2dq sin θ     rdθ=dr          =qπdθ
=K.qπr2π0sin θ dθ
=2kqπr2=12πϵ0qπr2(^J)

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