A long solenoid, with its axis along the x axis, consists of 230 turns per meter
ID: 1373538 • Letter: A
Question
A long solenoid, with its axis along the x axis, consists of 230 turns per meter of wire that carries a steady current of 15.0 A. A coil is formed by wrapping 30 turns of thin wire around a circular frame that has a radius of 6.00 cm. The coil is placed inside the solenoid and mounted on an axis that is a diameter of the coil and coincides with the y axis. The coil is then rotated with an angular speed of 3.00?rad/s. (The plane of the coil is in the yz plane at t = 0.)
A long solenoid, with its axis along the x axis, consists of 230 turns per meter of wire that carries a steady current of 15.0 A. A coil is formed by wrapping 30 turns of thin wire around a circular frame that has a radius of 6.00 cm. The coil is placed inside the solenoid and mounted on an axis that is a diameter of the coil and coincides with the y axis. The coil is then rotated with an angular speed of 3.00?rad/s. (The plane of the coil is in the yz plane at t = 0.) Determine the emf generated in the coil as a function of time. E = mVExplanation / Answer
Magnetic field inside the solenoid is
B = mu_o N I
= ( 4 pi *10^ -7 T /A ) ( 230 ) (15 A )
= 0.00433 T
Magnetic flux throug hthe coil
flux = NBA cos ( wt )
emf induced in the coil is
emf = N B A w sin ( w t)
= ( 30) (0.00433 T) (pi) ( 6*10^ -2 m ) ^2 (3 rad/s) sin (wt )
=0.0044 sin (wt )
= 4.4 sin (wt ) mV
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