Physics

Physics

Problem

The magnetic flux (in Wb) through a coil of one turn is given by Φ(t)=4t2−t\Phi(t)=4t^{2}-t, where tt is in seconds. a. (i) Find the instantaneous induced emf at t=2 st = 2\,\text{s}. b. (ii) Determine the average induced emf in the interval from t=1 st = 1\,\text{s} to t=3 st = 3\,\text{s}.
Intuitive explanation

The key is recognizing that induced EMF is the rate of change of magnetic flux—not the flux itself. Take the derivative of Φ(t)\Phi(t) with respect to time to find how quickly the flux is changing at any moment. This tells you the voltage induced in the coil, which is what the problem is really asking for when it mentions "one turn."

Intuitive explanation

The key is recognizing that induced EMF is the rate of change of magnetic flux—not the flux itself. Take the derivative of Φ(t)\Phi(t) with respect to time to find how quickly the flux is changing at any moment. This tells you the voltage induced in the coil, which is what the problem is really asking for when it mentions "one turn."

Browse the problem library