Question

A very long solenoid with a circular cross section and radius r₁= 1.20 cm with n_s= 230 turns/cm lies inside a short coil of radius r₂= 4.80 cm and N_c= 25 turns.

outer coil solenoid

A) If the current in the solenoid is ramped at a constant rate from zero to I_s= 1.10 A over a time interval of 45.0 ms, what is the magnitude of the emf in the outer coil while the current in the solenoid is changing?

B) What is the mutual inductance between the solenoid and the short coil?

C) Now reverse the situation. If the current in the short coil is ramped up steadily from zero to I_c= 2.00 A over a time interval of 13.0 ms, what is the magnitude of the emf in the solenoid while the current in the coil is changing?

Answer 1

B. Mutual inductance is given by, -4mx10-7H-m-1 x 230x102 turns-1n-1 x 25 turns x πΧ(0.012 m) = 3.27x10-4 H Hence, mutual inductance between the solenoid and the short coil is 327x10 H C. Induced emf in the inner coil is given by dI dt ΔΙ Ai m-, 25 turns 1x230 x 102 turns-m-1 x 2TX0.0 12 mx x0.048m)x_2A 13-10-5 0.20 V Hence, magnitude of induced emf in the inner coil is 0.2