A very long solenoid has 1.0 x 106 turns per meter and a cross-sectional area of

Question

A very long solenoid has 1.0 x 106 turns per meter and a cross-sectional area of 2.0 x 10-4 m2 . A short, secondary coil with 1.0 x 103 turns is wound over the solenoid's midpoint. What emf is induced in the secondary coil if the current in the solenoid is changing at a rate of 4.0 A/s? The answer is 1.0V, but I don't know how to work it out.
A very long solenoid has 1.0 x 106 turns per meter and a cross-sectional area of 2.0 x 10-4 m2 . A short, secondary coil with 1.0 x 103 turns is wound over the solenoid's midpoint. What emf is induced in the secondary coil if the current in the solenoid is changing at a rate of 4.0 A/s? The answer is 1.0V, but I don't know how to work it out.

Explanation / Answer

number of turns of solenoid per meter  n /l   = 1*10^ 6 turns / m crossectional area of solenoid    A = 2*10^ -4 m^2 Current in the solenoid   dI /dt = 4 A /s         Magnetic field of a solenoid                       B = µ_o n I          number of turns of secondary coil N = 1*10^ 3 turns        emf induced in the secondary coil                 e = d / dt ( BA N )                     = AN dB / dt                       = A N µ_o n dI /dt                      = ( 2*10^ -4 m^2)(1*10^ 3 turns )(1*10^ 6 turns / m )(4p*10^ -7 )(4 )                        = 100.48*10^ -2                        = 1 V

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