The magnetic flux through three different coils is changing as shown in Figure P21.16. For each

The magnetic flux through three different coils is changing...

Key Concepts

Magnetic Flux

Magnetic flux is a measure of the total magnetic field passing through a given area. It quantifies the number of magnetic field lines crossing a surface and is a fundamental parameter in understanding how magnetic fields interact with conductors. Changes in magnetic flux are central to inducing electrical effects in nearby circuits.

Induced Electromotive Force (emf)

Induced emf is a voltage generated in a conductor due to a change in magnetic flux through the conductor. This phenomenon is a key aspect of electromagnetic induction, where the rate of change of flux determines the magnitude of the induced voltage according to principles established by Faraday.

Faraday's Law of Induction

Faraday's law of induction states that an emf is induced in a circuit when there is a change in magnetic flux through it, with the magnitude of the emf proportional to the rate at which the flux changes. This law forms the basis for understanding how generators, transformers, and many electrical devices operate.

Lenz's Law

Lenz's law provides the direction of the induced emf and current resulting from a change in magnetic flux. It states that the induced current will flow in a direction that opposes the change in flux that produced it, thereby conserving energy and confirming the principle of action and reaction in electromagnetic processes.

Graphical Analysis of Time-Varying Quantities

Graphical analysis in the context of electromagnetic induction involves understanding how physical quantities like magnetic flux and induced emf change over time. By plotting these quantities against time, one can qualitatively and quantitatively analyze the behavior of systems undergoing electromagnetic induction, including identifying periods of rapid change and steady-state conditions.

Transcript

00:01 In the given problem, there are three different coils and we have been given the variation of magnetic flux with respect to time in all these three different coils.

00:16 In the first coil, this is the y -axis over which there is the variation of magnetic flux and the time is varying along x -axis.

00:38 And the curve given for this variation of magnetic flux is like this.

00:47 And corresponding to this magnetic flux versus time curve, we have to obtain emf -induced versus time curve.

01:03 And as we know, as per faraday's laws of electromagnetic -magnetive, induction, emf induced is given as negative of the time rate of change of magnetic flux.

01:16 Or we can say this is the negative of slope of the curve magnetic flux versus time.

01:31 So here in this given question, this slope is positive as the value of the flux is increasing to the passage of time.

01:42 Hence as a slope is positive.

01:45 So the emf induced will be negative and it will be having a constant value as a slope is constant.

01:54 So the variation of this emf respect to time may be given like this up to the given time interval.

02:11 And if the time will be increasing more and more, this emf induced will be.

02:17 Keep on increasing.

02:19 So this is the answer for this first part in which the magnetic flux has been represented passing through the first coil.

02:28 Now in the second coil, the magnetic flux is going on decreasing with the passage of time.

02:45 This is the time again.

02:47 Here this is the magnetic flux and this is decreasing in a manner like this.

02:55 So, if we plot the curves, if we plot the slopes at various points, here at the topmost point, the slope is almost zero and then this slope is going on increasing and every time it is having a negative value.

03:18 So again using the expression for the induced emf negative of slope...

Please give Ace some feedback