Question
If two coils placed next to one another have a mutual inductance of 5.00 mH, what voltage is induced in one when the 2.00 A current in the other is switched off in 30.0 ms?
Final Answer
Solution video
OpenStax College Physics for AP® Courses, Chapter 23, Problem 56 (Problems & Exercises)
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This is College Physics Answers with Shaun Dychko. The mutual inductance between these two coils tells us the extent to which a change in current in the first coil will cause an emf to be induced in the second coil. So the mutual inductance is 5.00 millihenries, which is 5.00 times 10 to the minus 3 henries; the change in current in the first coil is 2.00 amps because we are told that it starts with this current and then goes to zero so that means the change is 2.00 and it happens in a time of 30.0 milliseconds, which is 30.0 times 10 to the minus 3 seconds. So the induced emf in coil two is the mutual inductance between the coils multiplied by the rate of change of current in the first coil. So that's negative 5.00 times 10 to the minus 3 henries times 2.00 amps—change in current in the first coil—divided by 30.0 times 10 to the minus 3 seconds, which is a time over which that change from 2 to 0 amps occurs and this is negative 0.333 volts and the negative sign's not really that important here, it's just to indicate the direction of emf in coil two.