A metal ring is dropped into a localized region of constant...

A metal ring is dropped into a localized region of constant magnetic field, as indicated in Figure 23.23. The magnetic field is zero above and below the region. (a) At each of the three indicated locations ( 1,2 , and 3 ), is the induced current clockwise, counterclockwise, or zero? (b) Choose the best explanation from among the following: A. The induced current is clockwise at 1 to oppose the field, zero at 2 because the field is uniform, and counterclockwise at 3 to maintain the field. B. The induced current is counterclockwise at 1 to oppose the field, zero at 2 because the field is uniform, and clockwise at 3 to maintain the field. C. The induced current is clockwise at 1 to oppose the field, clockwise at 2 to maintain the field, and clockwise at 3 to oppose the field.

A metal ring is dropped into a localized region of constant magnetic field, as indicated in Figure 23.23. The magnetic field is zero above and below the region. (a) At each of the three indicated locations ( 1,2 , and 3 ), is the induced current clockwise, counterclockwise, or zero? (b) Choose the best explanation from among the following:
A. The induced current is clockwise at 1 to oppose the field, zero at 2 because the field is uniform, and counterclockwise at 3 to maintain the field.

B. The induced current is counterclockwise at 1 to oppose the field, zero at 2 because the field is uniform, and clockwise at 3 to maintain the field.

C. The induced current is clockwise at 1 to oppose the field, clockwise at 2 to maintain the field, and clockwise at 3 to oppose the field.

Key Concepts

Faraday's Law of Electromagnetic Induction

This law states that a changing magnetic flux through a circuit induces an electromotive force (emf) in the circuit. It is fundamental to understanding how motion or alterations in the magnetic environment of a conductor lead to the generation of electrical currents.

Lenz's Law

Lenz's Law provides the direction of the induced current, asserting that the current flows in a direction that opposes the change in magnetic flux that produced it. This opposition is crucial for maintaining energy conservation and explains why the induced current acts to counteract the original change in the magnetic environment.

Magnetic Flux

Magnetic flux is a measure of the amount of magnetic field passing through a given area. It plays a central role in electromagnetic induction, as variations in the flux—whether by changing the magnetic field strength, the area exposed to the field, or the orientation—are what cause the induction of emf in a circuit.

Uniform versus Non-Uniform Magnetic Fields

In contexts involving induced currents, the uniformity of the magnetic field is significant. When a conductor moves through a uniform magnetic field, the magnetic flux may remain constant, resulting in no induced current. In contrast, a non-uniform magnetic field, or transitions into and out of a field region, leads to changes in flux and thus induces current according to Faraday's Law.

Transcript

00:01 This question concerns electromagnetic induction.

00:06 In a question concerning induction, we often have to answer four questions.

00:12 Those questions are, which direction does the existing magnetic field point? now in this problem, we are shown circles with dots inside of them, which indicate that the magnetic field in this region points out of the plane of the page, and that's true for all three scenarios here.

00:36 So we've answered the first question.

00:40 The second question says, how is the magnetic flux changing the situation? so let's answer that for ring one.

00:49 Ring one is going into the field here.

00:55 So part of the ring is outside of the field and part of it's inside the field.

01:00 So the magnetic flux going through ring one is increasing, because the field is going through the plane of the ring there.

01:09 So the flux is increasing.

01:11 We've answered question two.

01:13 Now question three says, then which way should the induced field point? remember lenz's law says that an induced magnetic field will point in such a way as to oppose the change in flux.

01:27 Since the existing field is pointing out of the page, and since it's increasing, lenz's law says that an field should point into the page so as to oppose that.

01:39 And the fourth question is, okay, if that's the direction for your induced magnetic field, what direction should the current flow in order to cause that to happen? well, if we want to have a field going into the page, an induced field, we need to have, according to the right -hand rule, a clockwise current.

01:59 And so the answer for scenario one is going to be clockwise.

02:04 We've answered those four questions.

02:06 Let's do it for scenario two.

02:13 I'm going to erase this field here, or this ring i should say, because we're going to do it for a different ring now.

02:20 Our second ring is actually entirely contained within the field, and that's the key right there.

02:26 So the first question is still the same.

02:28 Which way is the existing field? out of the plane of the page.

02:32 Secondly, how is the magnetic flux changing? and the answer here is it's not changing.

02:38 And since the flux is not changing, there's no need to oppose or support the existing field, and so therefore there's going to be no induced field, and so therefore no induced current.

02:49 So for scenario two, where the ring is completely inside of our field, the answer is zero.

03:01 And for scenario three, well now we have our ring, but it's at the area with field, so it's leaving the area that has some magnetic field.

03:16 And so we answered the four questions again.

03:20 Which way is the existing field? still out of the page.

03:22 What is happening to the flux? it's decreasing...

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