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 150 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 15.0 ms

What was the initial flux through the small coil?

Determine the average induced emf in the small coil during the 15.0 ms

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.

During the 15.0 ms , what was the average current in the small coil, assuming it has a resistance of 0.100 ?

Explanation / Answer

a.)B=u0*N*I=0.1935 T

flux=BAcos(0)=BA=0.1935*pi*(4x10^-3)^2= 9.73 x 10^-6 Wb

b.)E=N(d(flux))/dt=150*9.73x10^-6/15x10^-3= 0.0973 V

c.)the flux through the coil decreases when the switch is opened, so direction of induced current is clockwise.

d.)E=IR

I=0.0973/0.1= 0.973 A

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