Physics-
General
Easy

Question

What is the mutual inductance of a two-loop system as shown with centre separation l

  1. fraction numerator mu subscript 0 end subscript pi a to the power of 4 end exponent over denominator 8 l to the power of 3 end exponent end fraction    
  2. fraction numerator mu subscript 0 end subscript pi a to the power of 4 end exponent over denominator 4 l to the power of 3 end exponent end fraction    
  3. fraction numerator mu subscript 0 end subscript pi a to the power of 4 end exponent over denominator 6 l to the power of 3 end exponent end fraction    
  4. fraction numerator mu subscript 0 end subscript pi a to the power of 4 end exponent over denominator 2 l to the power of 3 end exponent end fraction    

The correct answer is: fraction numerator mu subscript 0 end subscript pi a to the power of 4 end exponent over denominator 2 l to the power of 3 end exponent end fraction


    Magnetic field at the location of coil (b) produced due to coil (a)

    B subscript 1 end subscript equals fraction numerator mu subscript o end subscript over denominator 4 pi end fraction. fraction numerator 2 M over denominator l to the power of 3 end exponent end fraction
    Flux linked with coil ((b)
    phi subscript 2 end subscript equals B subscript 1 end subscript A subscript 2 end subscript equals fraction numerator mu subscript o end subscript over denominator 4 pi end fraction fraction numerator 2 i   left parenthesis pi a to the power of 2 end exponent right parenthesis over denominator l to the power of 3 end exponent end fraction cross times left parenthesis pi a to the power of 2 end exponent right parenthesis
    Also phi subscript 2 end subscript equals M i rightwards double arrow M equals fraction numerator mu subscript o end subscript pi a to the power of 4 end exponent over denominator 2 l to the power of 3 end exponent end fraction

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