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Moving Charges And Magnetism

Question
CBSEENPH12039591

A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs BC (radius = b) and DA (radius = a) of the loop are joined by two straight wires AB andCD. A steady current I is flowing in the loop. Angle made by AB and CD at the origin O is 30º. Another straight thin wire with steady current I1 flowing out of the plane of the paper is kept at the origin.



The magnitude of the magnetic field (2) due to the loop ABCD at the origin (O) is

  • zero

  • fraction numerator straight mu space left parenthesis straight b minus straight a right parenthesis over denominator 24 ab end fraction
  • fraction numerator straight mu subscript straight o straight I over denominator 4 space straight pi end fraction space open square brackets fraction numerator straight b minus straight a over denominator ab end fraction close square brackets
  • fraction numerator straight mu subscript 0 straight I over denominator 4 straight pi end fraction space open square brackets 2 left parenthesis straight b minus straight a right parenthesis space plus straight pi over 3 left parenthesis straight a plus straight b right parenthesis close square brackets

Solution

B.

fraction numerator straight mu space left parenthesis straight b minus straight a right parenthesis over denominator 24 ab end fraction straight B space equals space 1 over 12 space of space fraction numerator straight mu subscript 0 straight I over denominator 2 end fraction space open parentheses 1 over straight a minus 1 over straight b close parentheses
space equals space fraction numerator straight mu subscript 0 straight I space left parenthesis straight b minus straight a right parenthesis over denominator 24 space ab end fraction