Predict/Explain A metal ring is dropped into a localized...

Predict/Explain A metal ring is dropped into a localized region of constant magnetic field, as indicated in Figure $23-30$. The magnetic field is zero above and below the region where it is finite. (a) For 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: Clockwise at 1 to oppose the field; zero at 2 because the field is uniform; counterclockwise at 3 to try to maintain the field. II. Counterclockwise at 1 to oppose the field; zero at 2 because the field is uniform; clockwise at 3 to try to maintain the field. III. Clockwise at 1 to oppose the field; clockwise at 2 to maintain the field; clockwise at 3 to oppose the field.

Predict/Explain A metal ring is dropped into a localized region of constant magnetic field, as indicated in Figure $23-30$. The magnetic field is zero above and below the region where it is finite. (a) For 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: Clockwise at 1 to oppose the field; zero at 2 because the field is uniform; counterclockwise at 3 to try to maintain the field. II. Counterclockwise at 1 to oppose the field; zero at 2 because the field is uniform; clockwise at 3 to try to maintain the field.
III. Clockwise at 1 to oppose the field; clockwise at 2 to maintain the field; clockwise at 3 to oppose the field.

Key Concepts

Magnetic Flux

Magnetic flux is a measure of the quantity of magnetic field passing through a given area. It is the product of the magnetic field strength, the area perpendicular to the field, and the cosine of the angle between the field lines and the normal to the surface. Variations in magnetic flux over time are what drive the induction of an electromotive force as described by Faraday's Law.

Electromagnetic Induction

Electromagnetic induction is the phenomenon where a changing magnetic environment induces an electromotive force (emf) in a conductor. This principle is foundational to many electrical devices and systems, explaining how a moving conductor or a changing magnetic field can result in electric currents through coils, loops, or other conducting elements.

Faraday's Law

Faraday's Law states that the induced emf in a closed loop is equal to the negative rate of change of magnetic flux through the area enclosed by the loop. This quantitative relationship links the dynamics of magnetic fields with the generation of voltage, and it forms the mathematical basis for predicting the magnitude of induced currents.

Lenz's Law

Lenz's Law provides the direction of the induced current resulting from electromagnetic induction. It states that the induced current will flow in such a direction that the magnetic field it creates opposes the change in the original magnetic flux. This opposition is a reflection of the conservation of energy and ensures that the induced emf resists the flux change.

Transcript

00:01 In the given problem here.

00:03 This is a finite uniform magnetic field which is coming out perpendicularly through this plane of paper.

00:21 Now a metallic ring is allowed to fall through this region of magnetic field and we take its three different locations.

00:35 This is location 1, then here this is location 2, and finally here this is location 3 of the same ring falling through this field.

00:49 1, 2, and 3.

00:53 Now we have to find for each of these 3 locations, the direction of current induced and that is based upon the lenses.

01:11 Law which says that the direction of induced current and hence that of induced magnetic field is always such that it opposes the reason behind its induction or we can say the induced magnetic field is always opposite in sense to the inducing magnetic field.

02:23 Hence, in the first part of the problem, at location 1 as the coil is falling down, so the magnetic field which is outward in direction and that is increasing.

02:42 So the inducing magnetic field is outward increasing.

02:46 So the induced magnetic field will be inward increasing means magnet field should enter induced magnetic field should enter into the plane of coil and we know magnet field enters only into the south pole so the upper face of the coil should start behaving like south pole means the direction of current induced in it should be clockwise in location 1 then in location 2 as the coil is falling through uniform magnetic field so no change in magnetic field, hence that of magnetic flux...

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