An aluminum ring of radius 5.0 cm and resistance 6.0 × 10-4 is placed around the

Question

An aluminum ring of radius 5.0 cm and resistance 6.0 × 10-4 is placed around the top of a long air-core solenoid with 1004 turns per meter and a smaller radius of 3.0 cm, as in Figure P20.62. If the current in the solenoid is increasing at a constant rate of 265 A/s, what is the induced current in the ring? Assume that the magnetic field produced by the solenoid over the area at the end of the solenoid is one-half as strong as the field at the center of the solenoid. Assume also that the solenoid produces a negligible field outside its cross-sectional area 5.0 cm 3.0 em Figure P20.62

Explanation / Answer

Area,

              A = .r22

                  = 3.14 x (3*10-2)2

= 3.14 x 9x10-4

                  = 28.27x10-4 m2

The induced emf,

               = d/dt = 0.5 o.n.A.dI/dt

                = 2 x10-7 x1004 x 28.27 x10-4 x 265

                = 4.725 x 10-4 V

The induced current,

             I = /R

               = 4.725 x 10-4 / 6.0x10-4

               = 0.7875 A

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

                 Bc =  o.I / 2.r1

                       = (2 x10-7) x 0.787 / 5.0x10-2

                      = 9.89 x10-6 T

                      = 9.89 T

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