Two coils are placed near each other, and one is on top of the other one. The magnetic flux through thetop coil changes due to a varying current in the coil.(a) Suppose the magnetic flux through the top coil increases at a uniform rate of 0.3 Wb/s, what is theinduced emf in the bottom coil? Is it constant with time?(b) Suppose the magnetic flux through the top coil decreases at a varying rate of 0.5t Wb/s, what is theinduced emf in the bottom coil? Is it constant with time? What happens to the direction of thecurrent in the bottom coil, as compared with part a)?(c) Suppose that the current described in part a) is in the bottom coil rather than the top one. What isthe induced emf in the top coil?
Question
Two coils are placed near each other, and one is on top of the other one. The magnetic flux through thetop coil changes due to a varying current in the coil.(a) Suppose the magnetic flux through the top coil increases at a uniform rate of 0.3 Wb/s, what is theinduced emf in the bottom coil? Is it constant with time?(b) Suppose the magnetic flux through the top coil decreases at a varying rate of 0.5t Wb/s, what is theinduced emf in the bottom coil? Is it constant with time? What happens to the direction of thecurrent in the bottom coil, as compared with part a)?(c) Suppose that the current described in part a) is in the bottom coil rather than the top one. What isthe induced emf in the top coil?
Solution
(a) According to Faraday's law of electromagnetic induction, the induced emf in a coil is equal to the rate of change of magnetic flux through it. So, if the magnetic flux through the top coil increases at a uniform rate of 0.3 Wb/s, the induced emf in the bottom coil will be equal to this rate, i.e., 0.3 V. Since the rate of change of flux is constant, the induced emf will also be constant with time.
(b) If the magnetic flux through the top coil decreases at a varying rate of 0.5t Wb/s, the induced emf in the bottom coil will be equal to the derivative of this rate with respect to time, i.e., -0.5 V/s. Since the rate of change of flux is not constant, the induced emf will not be constant with time. According to Lenz's law, the direction of the induced current (and hence the induced emf) is such that it opposes the change in magnetic flux that produced it. So, if the flux is decreasing, the direction of the induced current will be opposite to that in part (a).
(c) If the current described in part (a) is in the bottom coil rather than the top one, the situation is essentially the same as in part (a), but with the roles of the coils reversed. According to Faraday's law, the induced emf in the top coil will be equal to the rate of change of magnetic flux through it, which is the same as the current in the bottom coil, i.e., 0.3 V.
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