A solenoid of length 50.0 cm is made of 11000 circular coils. It carries a stead

Question

A solenoid of length 50.0 cm is made of 11000 circular coils. It carries a steady current of 14.0 A . Near its center is placed a small, flat, circular metallic coil of 200 circular loops, each with a radius of 4.00 mm . This small coil is oriented so that it receives half of the maximum magnetic flux. A switch is opened in the solenoid circuit and its current drops to zero in 35.0 ms .

a) What was the initial flux through the small coil?

b) Determine the average induced emf in the small coil during the 35.0 ms .

c) If you look along the long axis of the solenoid so that the initial 14.0 A current is clockwise, determine the direction of the induced current in the small inner coil during the time the current drops to zero.

d) During the 35.0 ms , what was the average current in the small coil, assuming it has a resistance of 0.150 ?

Explanation / Answer

a) B = *n*I

   B= 4pi*10^-7*(11000/0.50)14.0= 0.387

    = BA*cos = 0.387*(pi*0.004^2)*cos(0)= 1.945 * 10^-5 Wb

b) [] = -N(/t) -200(1.945*10^-5/0.035)= 5.56*10^-4 V

c) CCW

d) Induced Current = I = /R = 5.56*10^-4/0.150 = 3.7 mA

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