You have the apparatus shown in Figure P18.14. A circular...

You have the apparatus shown in Figure P18.14. A circular metal plate swings past the north pole of a permanent magnet. The metal consists of a series of rings of increasing radius. Indicate the direction of the current in one ring (a) as the metal swings down from the left into the magnetic field and (b) as the metal swings up toward the right out of the magnetic field. Use Lenz’s law to justify your answers.

You have the apparatus shown in Figure P18.14. A circular metal plate swings past the north pole of a permanent magnet. The metal consists of a series of rings of increasing radius. Indicate the direction
of the current in one ring (a) as the metal swings down from the left into the magnetic field and (b) as the metal swings up toward the right out of the magnetic field. Use Lenz’s law to justify your answers.

Key Concepts

Electromagnetic Induction

This is the phenomenon by which a changing magnetic environment induces an electromotive force (emf) in a conductor. It forms the basis for many practical devices and is described quantitatively by Faraday’s law, which relates the rate of change in magnetic flux through a circuit to the magnitude of the induced emf.

Magnetic Flux

Magnetic flux represents the total magnetic field passing through a given area. Its measure takes into account both the strength of the magnetic field and the orientation of the area with respect to the field. Changes in magnetic flux over time are essential in inducing currents in a conductor.

Lenz’s Law

Lenz’s law states that the direction of an induced current in a conductor is such that the magnetic field created by the induced current opposes the change in the original magnetic flux. This opposition is a fundamental requirement for the conservation of energy within electromagnetic induction processes.

Eddy Currents

Eddy currents are loops of electrical current induced within conductors when they are exposed to changing magnetic fields. These currents create their own magnetic fields which oppose the changes that produced them, leading to effects such as magnetic braking. They are a direct application of electromagnetic induction and Lenz’s law in distributed systems like metallic plates or large solid conductors.

Transcript

00:01 In this question, we are asked to predict the direction of the induced current on the metal plate as it passes through a magnet whose north pole is facing towards the metal plate.

00:12 And we recognize that because the north pole is here, the magnetic field exerted by the magnet is going to be coming out of the page from our perspective.

00:22 And i will denote this magnetic field as the external magnetic field because it comes from an external force.

00:28 In order to solve this question, we have to understand lenses law, which states that the direction of the induced current, so i sub in, is such that it's induced b field, and i will write it as b sub in, opposes the change in the magnetic flux through the coil, the coil's area produced by other objects.

00:52 So let's look at how this law applies to this question.

00:56 Part a asks you, in the case where the metal plate is swinging downward and is passing through the external magnetic field produced by the magnet, what is happening to the induced current, if any? well, let's notice that in this case, the metal plate is experiencing an increase in the magnetic field because it is now entering the external magnetic field.

01:23 So there is all of a sudden an increase in the magnetic flux experienced by the metal plate.

01:30 So per linz's law, we're supposed to have an induced current that will eventually counter the effect of increasing magnetic flux.

01:40 So which direction must this induced current be so that it fits linz's law? well, let's recognize that because we want to decrease magnetic flux to counter this effect, we need to have an induced magnetic field that is in the opposite direction as the external magnetic field.

02:02 So i will denote this as the induced magnetic field and its direction is into the page from our perspective so that it opposes the external magnetic field direction.

02:16 So in a sense, it is trying to balance out the fact that the metal plate is experiencing an increase in magnetic flux...

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