Two coils have mutual inductance M = 3.25 × 10^-4 H. The current i1 in the first coil increases at a uniform rate of 830 A/s. (a) What is the magnitude of the induced emf in the second coil? Is it constant?

Video transcript

Welcome back. Everyone in this problem, two solenoids are placed such that their magnetic fields interact with each other. They have a mutual induction coefficient of M equals 4.32 multiplied by 10 to the negative fourth Henry, what is the magnitude of the induced EMF in solenoid two? If the current flowing through solenoid, one changes uniformly at a rate of 650 s per second. And is it constant? A says the induced EMF is 2.8 multiplied by 10 to the negative one volts and it is constant B says it's 3.1 multiplied by 10 to the negative one volts. And it's not constant. C says it's 4.5 multiplied by 10 to the negative one volts. And it is constant while D says it's 6.7 multiplied by 10 to the negative one volts and it's not constant. Now, let's first make note of the information we have so far, we know that the mutual induction coefficient M is 4.32 multiplied by 10 to the negative for Henry. OK. And we also know that the current through solenoid one changes at a rate of 650 amperes per second. Ok. So a change in current in solenoid one over time is going to be equal to 650 amperes per second. Now, how can we use this information to help us figure out the magnitude of the induced EMF what do we know about mutual indoctrinate? And EMF well, recall that the induced EMF in solenoid two due to the changing current in sole one is given by the formula that says it's the induced EMF equals the mutual inductance multiplied by or change in current over time. Now, here we have this information. OK? Because we know that the mutual inductance is 4.32 multiplied by 10 to the negative fourth Henry. And we know the change in current over time flowing through solenoid one is 650 S per second. So if we go ahead and multiply them, then we'll get the induced EMF in solenoid too. When we multiply, we get the ear F to be 0.2808 volts or written to two significant figures, approximately 2.8 multiplied. Let me write that eight properly, 2.8 multiplied by 10 to the negative one volts. Now remember in our problem, it also told us that our current flowing through solenoid one changes uniformly. So because the change of current is uniform, that means the induced AM F is going to be constant. Therefore, A is the correct answer. Thanks for watching everyone. I hope this video helped.