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Question

The magnetic induction at the centre O in the figure shown is

  1. fraction numerator mu subscript 0 end subscript i over denominator 4 end fraction open parentheses fraction numerator 1 over denominator R subscript 1 end subscript end fraction minus fraction numerator 1 over denominator R subscript 2 end subscript end fraction close parentheses    
  2. fraction numerator mu subscript 0 end subscript i over denominator 4 end fraction open parentheses fraction numerator 1 over denominator R subscript 1 end subscript end fraction plus fraction numerator 1 over denominator R subscript 2 end subscript end fraction close parentheses    
  3. fraction numerator mu subscript 0 end subscript i over denominator 4 end fraction open parentheses R subscript 1 end subscript minus R subscript 2 end subscript close parentheses    
  4. fraction numerator mu subscript 0 end subscript i over denominator 4 end fraction open parentheses R subscript 1 end subscript plus R subscript 2 end subscript close parentheses    

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


    In the following figure, magnetic fields at O due to section 1, 2, 3 and 4 are considered as B subscript 1 end subscript comma blank B subscript 2 end subscript comma blank B subscript 3 end subscript and B subscript 4 end subscript respectively
    B subscript 1 end subscript equals B subscript 3 end subscript equals 0
    B subscript 2 end subscript equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction bullet fraction numerator pi i over denominator R subscript 1 end subscript end fraction ⨂
    B subscript 4 end subscript equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction bullet fraction numerator pi i over denominator R subscript 2 end subscript end fraction ⨀ blank A s open vertical bar B subscript 2 end subscript close vertical bar greater than open vertical bar B subscript 4 end subscript close vertical bar
    So B subscript n e t end subscript equals B subscript 2 end subscript minus B subscript 4 end subscript rightwards double arrow B subscript n e t end subscript equals fraction numerator mu subscript 0 end subscript i over denominator 4 end fraction open parentheses fraction numerator 1 over denominator R subscript 1 end subscript end fraction minus fraction numerator 1 over denominator R subscript 2 end subscript end fraction close parentheses ⨂

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