1. If the current in the solenoid is ramped at a constant rate from zero to I s

Question

1. If the current in the solenoid is ramped at a constant rate from zero to Is= 2.80 A over a time interval of 76.0 ms, what is the magnitude of the emf in the outer coil while the current in the solenoid is changing?

2. What is the mutual inductance between the solenoid and the short coil?

3. Now reverse the situation. If the current in the short coil is ramped up steadily from zero to Ic= 3.00 A over a time interval of 29.0 ms, what is the magnitude of the emf in the solenoid while the current in the coil is changing?

A very long solenoid with a circular cross section and radius r1= 1.60 cm with ns= 160 turns/cm lies inside a short coil of radius r2= 3.70 cm and Nc= 23 turns.

Explanation / Answer

magnetic field due to a solenoid = uNI/L ; N/L can be taken as turns per unit length u is permeability and I is current

n = 160 turns per cm = 16000 turns per meter

B = 4*pi*10^-7 * 16000* i = 0.02 i

flux in solenoid = BA = 0.02i * (0.016)^2 = 5.14 *10^-6 * i

first let us find out the mutual inductance between the short coil and the solenoid

M = flux in the coil / current in solenoid

the solenoid is enclosed within the coil , so same flux flows between coil and solenoid

2)M = 5.14*10^-6 i / i = 5.14*10^-6 henry

1)now induced emf = Mdi/dt = 5.14 * 10^-6 * (2.8/76*10^-3) = 0.189 mV

3) even though you reverse the conditions M mutual inductance is fixed for a given configuration

so induced emf in solenoid is Mdi/dt = 5.14 *10^-6 * (3/29*10^-3) = 0.531 mV

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