Please answer all parts to this questions and explain how you got the answer! Th

Question

Please answer all parts to this questions and explain how you got the answer! Thank you!

A very long solenoid with a circular cross section and radius r1= 1.90 cm with ns= 230 turns/cm lies inside a short coil of radius r2= 3.40 cm and Nc= 46 turns.

A) If the current in the solenoid is ramped at a constant rate from zero to Is= 1.60 A over a time interval of 56.0 ms, what is the magnitude of the emf in the outer coil while the current in the solenoid is changing? Use Faraday's Law.

B) 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.

C) Now reverse the situation. If the current in the short coil is ramped up steadily from zero to Ic= 3.70 A over a time interval of 10.0 ms, what is the magnitude of the emf in the solenoid while the current in the coil is changing?

Explanation / Answer

magnetic field due to long solenoid B = uo*ns*I

magnetic flux through the short coil = B*A = Nc*B*pi*r1^2

induced emf = rate of change in flux

emf = Nc*B*pi*r1^2/t

emf = Nc*uo*ns*pi*r1^2*(dIs/dt)

emf = 46*4*pi*10^-7*23000*pi*0.019^2*1.6/0.056

emf = 0.043 V

=================

emf = M*dIs/dt

0.043 = M*1.6/0.056

M = 1.51*10^-3 H

===============================

emf = M*dIc/dt

emf = 1.51*10^-3*3.7/0.01

emf = 0.56 V

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