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Answer :
The electromagnetic force (emf) per unit length in a solenoid is given by -μ0*n*dI/dt where μ0 is the vacuum permeability, n is the number of turns per unit length, and dI/dt is the rate of change of current. Substituting the given values, we can calculate the induced emf. The induced emf per unit length is -0.02856 Tm^2/s.
The problem refers to a physics concept known as Faraday's Law of electromagnetic induction. According to Faraday's Law, the electromotive force (emf) in a circuit is proportional to the rate of change of magnetic flux.
In a long, cylindrical solenoid, the magnetic field (B) is given by μ0*n*I, where n is the number of turns per unit length, I is the current, and μ0 is the vacuum permeability (approximately 4π x 10^-7 Tesla meter/ampere).
The rate of change of the magnetic field (dB/dt) is μ0*n*dI/dt, and the induced emf per unit length (E/L) is given by --dB/dt, hence E/L = - μ0*n*dI/dt.
Substituting the given values: n = 98.2 turns/cm = 9820 turns/m, dI/dt = 7.32 A/s, and μ0 = 4π x 10^-7 Tm/A, we get E/L = -(4π x 10^-7 Tm/A) * (9820 turns/m) * (7.32 A/s), which when computed gives the induced emf per unit length.
Therefore, the induced emf per unit length is -0.02856 Tm^2/s.
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