(20) A long solenoid or radius R1 = 5 cm has n = 100 turns per cm. Centered with
ID: 1704712 • Letter: #
Question
(20) A long solenoid or radius R1 = 5 cm has n = 100 turns per cm. Centered within this solenoid is a 10 turn coil of radius R2 = 2.5 cm. A current of 10 A flowing through the outer solenoid is reduced to zero uniformly over a time of 5 seconds.A. What is the magnitude of the EMF that appears across the inner coil as the current is being reduced?
B. If, looking down along the axis of this system, the original current had been flowing counterclockwise, in what direction is the EMF in the inner coil. EXPLAIN your reasoning; a 50/50 guess at the right answer is worth no credit!
Explanation / Answer
Magnetic field as a function of current at center is
B = 0ni (n=100/cm, i-changes though time)
Flux in inner coil F=B*A*N = 0ni*R2^2*N (N=10)
a) EMF is equal to change of flux per unit time.
So EMF = -NA*dB/dt = R2^2*0n*N*di/dt (di/dt = -10A/5s = -2 A/s)
EMF = -*(2.5cm)2*4*10-7* V·s/(A·m)*100/cm*10*(-2A/s) = 4.93*10-4V.
b) main function of solenoid is trying to keep the flux constant.
when current in outer coil is counterclockwise and starting decrease, the inner coil generates current that gives magnetic field in same direction of outer coil, which is also in counterclockwise direction and icreasing.
Increasing of current in coil means that the EMF is in opposite direction.(with current)
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