Physics-
General
Easy

Question

A solenoid has 2000 turns wound over a length of 0.30 m. The area of its cross-section is 1.2 cross times 10 to the power of negative 3 end exponent m to the power of 2 end exponent. blankAround its central section a coil of 300 turns is wound. If an initial current of 2 A in the solenoid is reversed in 0.25s, the emf induced in the coil is

  1. 48 V  
  2. 4.8 V  
  3. 4.8cross times 10 to the power of negative 1 end exponent V  
  4. 4.8cross times 10 to the power of negative 2 end exponent V  

The correct answer is: 48 V


    The induced emf is given by
    e equals negative M fraction numerator d i over denominator d t end fraction…(i)
    Where Mis coefficient of mutual inductance, fraction numerator d i over denominator d t end fraction is rate of change of current.
    Also, mutual inductance of two coaxial solenoids is given by
    M equals fraction numerator mu subscript 0 end subscript N subscript 1 end subscript N subscript 2 end subscript A over denominator l end fraction…(ii)

    From Eqs. (i) and (ii), we get
    e equals fraction numerator mu subscript 0 end subscript N subscript 1 end subscript N subscript 2 end subscript A over denominator l end fraction cross times fraction numerator d i over denominator d t end fraction
    Given, N subscript 1 end subscript equals 2000 comma N subscript 2 end subscript equals 300 comma A equals 1.2 cross times 10 to the power of negative 3 end exponent m to the power of 2 end exponent
    fraction numerator d i over denominator d t end fraction equals fraction numerator 2 minus left parenthesis negative 2 right parenthesis over denominator 0.25 end fraction equals fraction numerator 4 over denominator 0.25 end fraction
    therefore e equals fraction numerator 4 pi cross times 10 to the power of negative 7 end exponent cross times 2000 cross times 300 cross times 1.2 cross times 10 to the power of negative 3 end exponent cross times 4 over denominator 0.3 cross times 0.25 end fraction
    rightwards double arrow e equals fraction numerator 4 cross times 3.14 cross times 2 cross times 3 cross times 1.2 cross times 4 cross times 10 to the power of negative 5 end exponent over denominator 0.3 cross times 0.25 end fraction
    rightwards double arrow open vertical bar e close vertical bar equals 4.8 cross times 10 to the power of negative 2 end exponent V

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