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Question

Figure shows the cross-sectional view of the hollow cylindrical conductor with inner radius 'R' and outer radius '2R', cylinder carrying uniformly distributed current along it's axis. The magnetic induction at point 'P' at a distance fraction numerator 3 R over denominator 2 end fractionfrom the axis of the cylinder will be

  1. Zero    
  2. fraction numerator 5 mu subscript 0 end subscript i over denominator 72 pi R end fraction    
  3. fraction numerator 7 mu subscript 0 end subscript i over denominator 18 pi R end fraction    
  4. fraction numerator 5 mu subscript 0 end subscript i over denominator 36 pi R end fraction    

The correct answer is: fraction numerator 5 mu subscript 0 end subscript i over denominator 36 pi R end fraction


    By using B equals fraction numerator mu subscript 0 end subscript i over denominator 2 pi r end fraction open parentheses fraction numerator r to the power of 2 end exponent minus a to the power of 2 end exponent over denominator b to the power of 2 end exponent minus a to the power of 2 end exponent end fraction close parentheses here r equals fraction numerator 3 R over denominator 2 end fraction comma a equals R comma b equals 2 R
    rightwards double arrow blank B equals fraction numerator mu subscript 0 end subscript i over denominator 2 pi open parentheses fraction numerator 3 R over denominator 2 end fraction close parentheses end fraction cross times open curly brackets fraction numerator open parentheses fraction numerator 3 R over denominator 2 end fraction close parentheses to the power of 2 end exponent minus R to the power of 2 end exponent over denominator left parenthesis 2 R to the power of 2 end exponent right parenthesis minus R to the power of 2 end exponent end fraction close curly brackets equals fraction numerator 5. mu subscript o end subscript i over denominator 36 pi r end fraction.

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