Physics-
General
Easy

Question

In the following figure a wire bent in the form of a regular polygon of n sides is inscribed in a circle of radius a. Net magnetic field at centre will be

  1. fraction numerator mu subscript 0 end subscript i over denominator 2 pi a end fraction tan invisible function application fraction numerator pi over denominator n end fraction    
  2. fraction numerator mu subscript 0 end subscript n i over denominator 2 pi a end fraction tan invisible function application fraction numerator pi over denominator n end fraction    
  3. fraction numerator 2 over denominator pi end fraction fraction numerator n i over denominator a end fraction mu subscript 0 end subscript tan invisible function application fraction numerator pi over denominator n end fraction    
  4. fraction numerator n i over denominator 2 a end fraction mu subscript 0 end subscript tan invisible function application fraction numerator pi over denominator n end fraction    

The correct answer is: fraction numerator mu subscript 0 end subscript n i over denominator 2 pi a end fraction tan invisible function application fraction numerator pi over denominator n end fraction


    Magnetic field at the centre due to one side

    B subscript 1 end subscript equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction. fraction numerator 2 i sin invisible function application theta over denominator r end fractionwhere r equals a cos invisible function application theta
    So B subscript 1 end subscript equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction. fraction numerator 2 i sin invisible function application theta over denominator a cos invisible function application theta end fraction equals fraction numerator mu subscript 0 end subscript i over denominator 2 pi a end fraction tan invisible function application theta
    Hence net magnetic field
    B subscript n e t end subscript equals n cross times fraction numerator mu subscript 0 end subscript i over denominator 2 pi a end fraction tan invisible function application fraction numerator pi over denominator n end fraction.

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