Physics-
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Question

A cell is connected between the points A and C of a circular conductor ABCD with O as centre and angle A O C equals 60 degree. If B subscript 1 and B subscript 2 are the magnitudes of the magnetic fields at O due to the currents in  ABC and ADC respectively, then ratio fraction numerator B subscript 1 end subscript over denominator B subscript 2 end subscript end fraction is

  1. 1    
  2. 2    
  3. 5    
  4. 6    

The correct answer is: 5


    From Biot-Savart law the magnetic field at the centre is directly proportional to the length of current carrying segment.
    therefore fraction numerator B subscript 1 end subscript over denominator B subscript 2 end subscript end fraction equals fraction numerator l e n g t h blank o f blank A B C over denominator l e n g t h blank o f blank A D C end fraction
    equals fraction numerator a n g l e blank s u b t e n d e d blank b y blank A B C over denominator a n g l e blank s u b t e n d e d blank b y blank A D C end fraction
    equals fraction numerator left parenthesis 360 degree minus 60 degree right parenthesis over denominator 60 degree end fraction equals fraction numerator 300 over denominator 60 end fraction equals fraction numerator 5 over denominator 1 end fraction

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