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Question

Find the magnetic induction of the field at the point O of a loop with current I, whose shape is illustrated in fig. the radius a and the side b are known

  1. fraction numerator mu subscript 0 end subscript I over denominator 3 pi end fraction open parentheses fraction numerator 3 pi over denominator 2 a end fraction plus fraction numerator square root of 2 over denominator b end fraction close parentheses    
  2. fraction numerator mu subscript 0 end subscript I over denominator 4 pi end fraction open parentheses fraction numerator 3 pi over denominator 4 a end fraction plus fraction numerator square root of 2 over denominator 2 b end fraction close parentheses    
  3. fraction numerator mu subscript 0 end subscript I over denominator 2 pi end fraction open parentheses fraction numerator 2 pi over denominator 3 a end fraction plus fraction numerator square root of 2 over denominator b end fraction close parentheses    
  4. fraction numerator mu subscript 0 end subscript I over denominator 2 pi end fraction open parentheses fraction numerator 3 pi over denominator 4 a end fraction plus fraction numerator square root of 2 over denominator b end fraction close parentheses    

The correct answer is: fraction numerator mu subscript 0 end subscript I over denominator 2 pi end fraction open parentheses fraction numerator 3 pi over denominator 4 a end fraction plus fraction numerator square root of 2 over denominator b end fraction close parentheses

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