Physics-
General
Easy

Question

The figure shows the cross-section of a long cylindrical conductor of radius a carrying a uniformly distributed current i. The magnetic field due to current at P is

  1. mu subscript 0 end subscript i r divided by left parenthesis 2 pi a to the power of 2 end exponent right parenthesis    
  2. mu subscript 0 end subscript i r to the power of 2 end exponent divided by left parenthesis 2 pi a right parenthesis    
  3. mu subscript 0 end subscript i a divided by left parenthesis 2 pi r to the power of 2 end exponent right parenthesis    
  4. mu subscript 0 end subscript i a to the power of 2 end exponent divided by left parenthesis pi r to the power of 2 end exponent right parenthesis    

The correct answer is: mu subscript 0 end subscript i r divided by left parenthesis 2 pi a to the power of 2 end exponent right parenthesis


    The current enclosed with in the circle
    fraction numerator i over denominator pi a to the power of 2 end exponent end fraction blank comma blank pi r to the power of 2 end exponent equals fraction numerator i over denominator a to the power of 2 end exponent end fraction r to the power of 2 end exponent
    Ampere’s law not stretchy contour integral B. d l equals mu subscript 0 end subscript i ´ gives
    B blank.2 pi r equals fraction numerator mu subscript 0 end subscript i r to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction
    or B equals blank fraction numerator mu subscript 0 end subscript i r over denominator 2 pi a to the power of 2 end exponent end fraction

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