An aluminium ring of radius r_1 = 5.00 cm and a resistance of 3.75 times 10^-4 O

Question

An aluminium ring of radius r_1 = 5.00 cm and a resistance of 3.75 times 10^-4 Omega is placed around one end of a long air-corn solenoid with 1 020 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 field 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

Well, the above rating, (2 KP) is not very encouraging togrind thru the calculations.

But I will do it. Not quite sure of its accuracy You check thesteps and simplifications.

Area,               A = .r22 = 3.14x9x10-4 = 28.26x10-4 m2

The induced emf,                = d/dt = 0.5 o.n.A.dI/dt                

= 2 x10-7 x1020 x28.26 x10-4 x270                 = 4.89 x 10-4 V

The induced current,              I = /R = 4.89 x 10-4/3.75x10-4                 = 1.30A

(b) Thje magnetic field at the centre of the Al ring,                

  Bc =  o.I/2.r1 =2 x10-7x1.30/5.0x10-2                       = 1.63x10-5 T = 16.3 T   

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