Referring to Figure 23.57(a), what is the direction of the current induced in coil 2: (a) If the

Referring to Figure 23.57(a), what is the direction of the...

Key Concepts

Magnetic Flux

Magnetic flux is a measure of the amount of magnetic field passing through a given area, particularly through a coil or loop of wire. Understanding magnetic flux is essential to determine the impact of the varying magnetic fields on the induced EMF and current, as changes in flux directly influence the induction process.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the induced current or magnetic field. By aligning your thumb and fingers according to the established rules, you can visualize the relationship between the changing magnetic flux, the induced magnetic field, and the resultant current direction, which is key to applying Lenz's Law in practice.

Faraday's Law of Induction

This law states that a changing magnetic flux through a circuit produces an electromotive force (EMF) in the circuit. It quantitatively relates the rate of change of magnetic flux to the induced voltage, forming the foundational understanding of how and why currents are induced in coils when the magnetic environment changes.

Lenz's Law

Lenz's Law provides the direction of the induced current, asserting that the induced magnetic field created by this current opposes the change in the original magnetic flux. This opposition is a consequence of energy conservation and is crucial for predicting how a circuit reacts to increasing or decreasing magnetic fields.

Transcript

00:01 In this problem, we have a kind of a ring or a coil of wire, and we have a current flowing in it here.

00:13 And then we have a second coil of wire over here.

00:16 And we want to know how the current in here induces current over here.

00:22 So we'll use lenz's law, which basically says that a current is induced to oppose any change in the magnetic field.

00:29 Of that is exposed to it.

00:35 So in this first wire, where we have a current flowing, we know we have a magnetic field that's coming out of the page.

00:42 So this is an arrow here, the dot saying that it's coming out of the page, just from the right -hand rule.

00:50 So in the first case, they tell us that this current is increasing, which means that the magnitude of this electric field, magnetic field is also increasing.

01:05 Now this coil over here doesn't like is obviously experiencing some of this magnetic field because they're close enough together.

01:14 And it, you can think of it as it doesn't like this change.

01:18 So it doesn't want this change.

01:21 And to feel a change in the magnetic field, it's kind of going to oppose that.

01:26 So to oppose that, it would actually create a current in the magnetic field.

01:29 It's kind of going to oppose that.

01:29 So to oppose that, it would actually create a current in the magnetic field.

01:32 The clockwise direction so that we have an electric field or magnetic field going into the page.

01:38 So the one coming out of the page is growing.

01:44 So we're trying to keep the one going into the page is also going to be growing so that we can try to maintain a constant magnetic field.

01:58 So again, we generate a current that resists the change that this, this loop of wire is feeling from the magnetic field from this ring.

02:10 So in the second part of the problem, they're saying that, okay, now we have a, a, electric current that is decreasing in this wire.

02:20 So it's, in that case, this magnetic field is going to be getting lower over time.

02:27 So it's going to be shrinking.

02:30 And so this one, again, doesn't want to, doesn't like that, that, that magnetic field.

02:35 Field is shrinking around it...

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