A very long solenoid with a circular cross section and radius r_1 = 1.10 cm with

Question

A very long solenoid with a circular cross section and radius r_1 = 1.10 cm with n_s = 150 turns/cm lies inside a short coil of radius r_2 = 4.60 cm and N_c = 36 turns. If the current in the solenoid is ramped at a constant rate from zero to I_s =1.80 A over a time interval of 54.0 ms, what is the magnitude of the emf in the outer coil while the current in the solenoid is changing? Use Faraday's Law. What is the mutual inductance between the solenoid and the short coil? Look up the definition of mutual inductance. You already did most of the work in the previous problem. Now reverse the situation. If the current in the short coil is ramped up steadily from zero to I_c = 3.10 A over a time interval of 26.0 ms, what is the magnitude of the emf in the solenoid while the current in the coil is changing? 3.08 times 10^-2 V

Explanation / Answer

(a)

lnduced emf in outer coil,

emf = M*dl / dt

M =  u0*N*n*A2

where, A2 = area of outer coil

M = 4*pi*10^(-7)*36*15000*3.14*(0.046)^2

M = 0.0045 H

dl / dt = 1.80 / 0.054 = 33.33

emf = 0.0045 * 33.33 = 0.150 V

(b)

mutual induction b/w solenoid and short coil,

M = u0*N*n*A1

M = 0.000257 = 0.257 mH

(c)

dl / dt = 3.1 / 0.026 = 119.23 A/s

emf in solenoid,

e = u0*N*n*A1*dl/ dt

e =  4*pi*10^(-7)*36*15000*3.14*(0.011)^2*119.23

e = 0.0308 V

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