Two coils, held in fixed positions, have a mutual inductance of 165 µH. What is the peak emf in one coil when the current in the other coil is I(t) = 16.0 sin(1.15 103t), where I is in amperes and t is in seconds?
Just a few hints on how to start it off would be very appreciated, thank you.
To find the peak emf in one coil, we can use Faraday's Law of Electromagnetic Induction. Here are a few steps to get started:
1. Recall Faraday's Law: The induced emf in a coil is equal to the rate of change of magnetic flux through the coil.
2. The mutual inductance (M) between two coils is a measure of the coupling between them. It tells us how much of the magnetic field created by one coil passes through the other coil. In this case, the mutual inductance is given as 165 µH.
3. Since the mutual inductance is given, we can use it to relate the change in magnetic flux (∆Φ) to the induced emf (∆emf) in the other coil using the formula: ∆emf = -M∆I/dt.
4. We are given the current in the other coil, I(t) = 16.0 sin(1.15 103t), where I is in amperes and t is in seconds. To find the change in current (∆I), we need to differentiate this equation with respect to time.
Once you have the derivative of I(t), you can substitute it into the formula for ∆emf and solve for the peak emf.
The peak emf is the mutual inductance TIMES the maximum rate of change of current in the other coil. That you get from the derivative of the current there.
That max dI/dt is 16*1150 amp/s