Physics-
General
Easy

Question

In the figure shown there are two semicircles of radii r subscript 1 end subscript and r subscript 2 end subscript in which a current i is flowing. The magnetic induction at the centreO will be

  1. fraction numerator mu subscript 0 end subscript i over denominator r end fraction left parenthesis r subscript 1 end subscript plus r subscript 2 end subscript right parenthesis    
  2. fraction numerator mu subscript 0 end subscript i over denominator 4 end fraction left parenthesis r subscript 1 end subscript minus r subscript 2 end subscript right parenthesis    
  3. fraction numerator mu subscript 0 end subscript i over denominator 4 end fraction open parentheses fraction numerator r subscript 1 end subscript plus r subscript 2 end subscript over denominator r subscript 1 end subscript r subscript 2 end subscript end fraction close parentheses    
  4. fraction numerator mu subscript 0 end subscript i over denominator 4 end fraction open parentheses fraction numerator r subscript 2 end subscript minus r subscript 1 end subscript over denominator r subscript 1 end subscript r subscript 2 end subscript end fraction close parentheses    

The correct answer is: fraction numerator mu subscript 0 end subscript i over denominator 4 end fraction open parentheses fraction numerator r subscript 1 end subscript plus r subscript 2 end subscript over denominator r subscript 1 end subscript r subscript 2 end subscript end fraction close parentheses


    The magnetic induction due to both semicircular parts will be in the same direction perpendicular to the paper inwards
    therefore B equals B subscript 1 end subscript plus B subscript 2 end subscript equals fraction numerator mu subscript 0 end subscript i over denominator 4 r subscript 1 end subscript end fraction plus fraction numerator mu subscript 0 end subscript i over denominator 4 r subscript 2 end subscript end fraction equals fraction numerator mu subscript 0 end subscript i over denominator 4 end fraction open parentheses fraction numerator r subscript 1 end subscript plus r subscript 2 end subscript over denominator r subscript 1 end subscript r subscript 2 end subscript end fraction close parentheses ⨂

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