An aluminum ring of radius r_1 = 5.00 cm and a resistance of 4.15 times 10^-4 Oh

Question

An aluminum ring of radius r_1 = 5.00 cm and a resistance of 4.15 times 10^-4 Ohm is placed around one end of a long air-core solenoid with 960 turns per meter and radius r_2 = 3.00 cm as shown in the figure below. Assume the axial component of the field produced by the solenoid is one-half as strong over the area of the end of the solenoid as at the center of the solenoid. Also assume the solenoid produces negligible Held outside its cross-sectional area. The current in the solenoid is increasing at a rate of 270 A/s. What is the induced current in the ring? A At the center of the ring, what is the magnitude of the magnetic field produced by the induced current in the ring? mu T

Explanation / Answer

Here , for the induced current in the ring

a) induced current in the loop = rate of change in flux/R

induced current in the loop = pi * 0.03^2 * 4pi *10^-7 * 960 * 270/(4.15 *10^-4)

induced current in the loop = 2.21 A

b)

magnetic field = u0 * I/(2R)

magnetic field = 4pi *10^-7 * 2.21/(2 * 0.05)

magnetic field = 2.78 *10^-5 T

magnetic field= 27.8 uT

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