Physics-
General
Easy

Question

Current I is flowing in conductor shaped as shown in the figure. The radius of the curved part is r and the length of straight portion is very large. The value of the magnetic field at the centre O will be

  1. fraction numerator mu subscript 0 end subscript I over denominator 4 pi r end fraction open parentheses fraction numerator 3 pi over denominator 2 end fraction plus 1 close parentheses    
  2. fraction numerator mu subscript 0 end subscript I over denominator 4 pi r end fraction open parentheses fraction numerator 3 pi over denominator 2 end fraction minus 1 close parentheses    
  3. fraction numerator mu subscript 0 end subscript I over denominator 4 pi r end fraction open parentheses fraction numerator pi over denominator 2 end fraction plus 1 close parentheses    
  4. fraction numerator mu subscript 0 end subscript I over denominator 4 pi r end fraction open parentheses fraction numerator pi over denominator 2 end fraction minus 1 close parentheses    

The correct answer is: fraction numerator mu subscript 0 end subscript I over denominator 4 pi r end fraction open parentheses fraction numerator 3 pi over denominator 2 end fraction plus 1 close parentheses


    B subscript A end subscript equals 0

    B subscript B end subscript equals blank fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator left parenthesis 2 pi minus pi divided by 2 right parenthesis I over denominator r end fraction blank circled times equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 3 pi I over denominator 2 r end fraction
    B subscript C end subscript equals fraction numerator mu subscript 0 end subscript I over denominator 4 pi r end fraction circled times
    So, net magnetic field at the centre
    equals B subscript A end subscript plus B subscript B end subscript plus blank B subscript C end subscript
    equals 0 plus fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 3 pi I over denominator 2 r end fraction plus fraction numerator mu subscript 0 end subscript I over denominator 4 pi r end fraction equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator I over denominator r end fraction open parentheses fraction numerator 3 pi over denominator 2 end fraction plus 1 close parentheses

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C a s e space i comma space w h e n space x greater or equal than 0
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