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 −q4π2ϵ0r2^jq2π2ϵ0r2^jq4π2ϵ0r2^j−q2π2ϵ0r2^j

Solution

## The correct option is D −q2π2ϵ0r2^jThe electric field can be written as, E=∫dE sin θ         q→πr                                                  dq→dr =∫Kdqr2sinθ       qπr=dqdr⇒dq=qπrdr =Kr2∫dq sin θ     rdθ=dr          =qπdθ =K.qπr2∫π0sin θ dθ =2kqπr2=12πϵ0qπr2(−^J)

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