Question

shows the time evolution of a uniform magnetic field. four particular instants labeled ta to td are also identified on the graph. the field passes through a circular coil whose normal is parallel to the direction of the field. at what time does the current induced in the coil have the largest value?

Answer 1

The current induced in a circular coil will reach its largest value when the rate of change of the magnetic field is greatest. This corresponds to the time when the slope of the field vs. time graph is the steepest.

Step-by-step explanation:

In the scenario presented, the current induced in the circular coil will reach its largest value when the rate of change of the magnetic field is greatest, as per Faraday's Law of electromagnetic induction which states that the induced electromotive force (EMF) in a closed circuit is equal to the rate of change of the magnetic flux through the circuit.

Therefore, if you are observing a graph showing the time evolution of a uniform magnetic field passing through your coil, you should look for the steepest slope (either positive or negative), because this represents the greatest rate of change of the magnetic field. At this time, the current induced in the circular coil would reach its largest value.

Remember that the direction of the induced current is such that it opposes the change in magnetic flux that produced it, in accordance with Lenz's law.

Learn more about Electromagnetic Induction