Physics-
General
Easy

Question

In the figure shown a square loop PQRS of side 'a' and resistance 'r' is placed near an infinitely long wire carrying a constant current I. The sides PQ and RS are parallel to the wire. The wire and the loop are in the same plane. The loop is rotated by 180 to the power of ring operator end exponent about an axis parallel to the long wire and passing through the mid points of the side QR and PS. The total amount of charge which passes through any point of the loop during rotation is :

  1. fraction numerator mu subscript 0 end subscript I a over denominator 2 pi r end fraction l n 2    
  2. fraction numerator mu subscript 0 end subscript I a over denominator pi r end fraction l n 2    
  3. fraction numerator mu subscript 0 end subscript I a to the power of 2 end exponent over denominator 2 pi r end fraction    
  4. cannot be found because time of rotation not give.    

The correct answer is: fraction numerator mu subscript 0 end subscript I a over denominator pi r end fraction l n 2


    q equals integral I d t equals integral negative fraction numerator 1 over denominator r end fraction fraction numerator d phi over denominator d t end fraction d t equals negative fraction numerator capital delta phi over denominator r end fraction equals fraction numerator mu subscript 0 end subscript I a over denominator pi I end fraction l n 2.

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