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Question

Figure shows a straight wire of length l current i. The magnitude of magnetic field produced by the current at point P is

  1. fraction numerator square root of 2 mu subscript 0 end subscript i over denominator pi l end fraction    
  2. fraction numerator mu subscript 0 end subscript i over denominator 4 pi l end fraction    
  3. fraction numerator square root of 2 mu subscript 0 end subscript i over denominator 8 pi l end fraction    
  4. fraction numerator mu subscript 0 end subscript i over denominator 2 square root of 2 pi l end fraction    

The correct answer is: fraction numerator square root of 2 mu subscript 0 end subscript i over denominator 8 pi l end fraction


    The given situation can be redrawn as follow.

    As we know the general formula for finding the magnetic field due to a finite length wire
    B equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction. fraction numerator i over denominator r end fraction left parenthesis sin invisible function application phi subscript 1 end subscript plus sin invisible function application phi subscript 2 end subscript right parenthesis
    Here phi subscript 1 end subscript equals 0 to the power of o end exponent comma   phi equals 4 5 to the power of o end exponent
    therefore B equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction. fraction numerator i over denominator r end fraction left parenthesis sin invisible function application 0 to the power of o end exponent plus sin invisible function application 4 5 to the power of o end exponent right parenthesis equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction. fraction numerator i over denominator square root of 2 l end fraction rightwards double arrow B equals fraction numerator square root of 2 mu subscript 0 end subscript i over denominator 8 pi l end fraction

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