Problem 21.08 A very long, straight solenoid with a diameter of 3.00 cm is wound

Question

Problem 21.08 A very long, straight solenoid with a diameter of 3.00 cm is wound with 40 turns of wire per centimeter, and the windings carry a current of 0.275 A . A second coil having N turns and a larger diameter is slipped over the solenoid so that the two are coaxial. The current in the solenoid is ramped down to zero over a period of 0.7 s.

Part A: What average emf is induced in the second coil if it has a diameter of 4.40 cm and N = 32? Express your answer in microvolts to two significant figures.

Part B: What is the induced emf if the diameter is 8.80 cm and N = 64? Express your answer in volts to two significant figures.

Explanation / Answer

  For a solenoid the magnetic field H=nI where n is the number of turns per unit length
Therefore H due to the solenoid= 40T/cm x 0.275 A= 11 AT/cm
The magnetic flux density B= 4xpix10^-7x11x10^3 AT/m=0.0138 wb/m2
Flux=0.0138x3x10^-4=4.14x10^-6
Rate of change of flux= 4.14x10^-6/0.7=5.91x10^-6
By Faraday's law emf=Nx5.91x10^-6

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