The magnetic flux through three different coils is changing as shown in Figure P 18.18 . For eac

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

Key Concepts

Lenz's Law

Lenz's Law provides the direction of the induced current generated by a changing magnetic flux. It states that the induced current will flow in such a direction that its own magnetic field opposes the change in the original magnetic flux, thereby preserving energy conservation within the system.

Graphical Interpretation of Induced emf

Graphing the induced emf involves understanding its relationship to the rate of change of magnetic flux over time. A steady magnetic flux produces zero induced emf, while rapid changes in flux result in higher emf values. Plotting these variations helps visualize how different flux change patterns affect the resulting induced emf, with the graph serving as a derivative representation of the flux variation.

Electromagnetic Induction

Electromagnetic induction is the process by which a change in magnetic flux through a circuit induces an electromotive force (emf). This phenomenon is the basis for the operation of many electrical devices such as generators and transformers, and it demonstrates the fundamental link between electricity and magnetism.

Magnetic Flux

Magnetic flux is a measure of the quantity of magnetic field lines passing through an area. It is an essential concept in electromagnetism, calculated as the product of the magnetic field strength, the area, and the cosine of the angle between the field direction and the normal to the surface. This concept underlies the analysis of how flux changes can induce electrical effects in conductors.

Faraday's Law of Electromagnetic Induction

Faraday's Law quantifies the induced emf as proportional to the rate of change of magnetic flux through a circuit. Expressed mathematically as emf = -d?/dt, this law forms the cornerstone of understanding how and why an induced emf arises when the magnetic environment of a conductor changes over time.

Transcript

00:01 In this question, we are given three different coils, three different situations, and for each coil, the magnetic flux versus time graph is given, and we are being asked to draw the corresponding graph showing quantitatively how the induced emf changes over time.

00:18 So let's start with the first scenario.

00:20 Before we can draw the corresponding graph, we have to understand the relationship between magnetic flux and induced emf.

00:29 So the induced emf is proportional to the negative of the change in flux over the changing time.

00:39 In other words, the magnitude of induced emf is actually the negative slope of the magnetic flux versus time graph.

00:48 So since we do have the flux versus time graph, this question turns out to be rather easy.

00:54 The first step is that we have to find the slope for each of the segment.

00:59 So the first slope, first segment right here is rise over run.

01:03 So you have rise being 0 .2, run being 2.

01:08 So 0 .2 divided by 2 is 0 .1.

01:12 Well, in this case, you have negative slope.

01:16 So in order to get to the induced emf, you have to make it positive, right? because your emf is the opposite of the slope of this graph.

01:28 And so the value for emf in this case is actually positive point one.

01:33 And so you can just go ahead and draw saying that this is going to be positive point one.

01:42 And you just draw a straight line from zero to two seconds.

01:48 Now from two seconds to four seconds, the slope here is obviously zero.

01:53 And zero is neither positive nor negative.

01:55 So all you have to do is draw a straight horse.

01:59 Line from two seconds to four seconds on this graph.

02:03 So that's it for the first scenario.

02:07 Let's keep going for the second scenario.

02:09 In this case, we have a different graph and we notice that the slope here is positive and rise over run we have 0 .4 divided by 1.

02:23 So the slope here is 0 .4, which means by the time you are going to draw the emf, you have to make it into negative point four from zero to one seconds.

02:36 So i am just going to denote this as negative point four on the graph, and i'm going to draw a straight line from zero to one seconds.

02:49 Now, from one to two seconds, this is zero slope, and zero is neither positive nor negative, so that's what the emf will be like...

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