A solenoid of radius b and length l has another smaller solenoid inside it. This smaller solenoid has radius a and length e. Both solenoids share the same central axis. The larger one has № total turns, and the smaller one has a total turns. (a) Picture just the larger solenoid by itself. What is the magnetic field inside it when a current Io is run through its wires? (b) Now bring the smaller solenoid back into the picture while a steady current Io continues to flow through the larger solenoid. What is the total magnetic flux through the smaller solenoid? (c) Finally, imagine the current running through the larger solenoid now has some time dependence of the form I(t) = I cos(wt). What is the induced current in the smaller solenoid?

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A solenoid of radius b and length l has another smaller solenoid inside it. This smaller solenoid has
radius a and length e. Both solenoids share the same central axis. The larger one has № total turns, and
the smaller one has a total turns. (a) Picture just the larger solenoid by itself. What is the magnetic
field inside it when a current Io is run through its wires? (b) Now bring the smaller solenoid back into the
picture while a steady current Io continues to flow through the larger solenoid. What is the total magnetic
flux through the smaller solenoid? (c) Finally, imagine the current running through the larger solenoid
now has some time dependence of the form I(t) = I cos(wt). What is the induced current in the smaller
solenoid?
Transcribed Image Text:A solenoid of radius b and length l has another smaller solenoid inside it. This smaller solenoid has radius a and length e. Both solenoids share the same central axis. The larger one has № total turns, and the smaller one has a total turns. (a) Picture just the larger solenoid by itself. What is the magnetic field inside it when a current Io is run through its wires? (b) Now bring the smaller solenoid back into the picture while a steady current Io continues to flow through the larger solenoid. What is the total magnetic flux through the smaller solenoid? (c) Finally, imagine the current running through the larger solenoid now has some time dependence of the form I(t) = I cos(wt). What is the induced current in the smaller solenoid?
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