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A circular loop of wire is in a spatially uniform magnetic field, as shown in Figure $21.51 .$ The magnetic field is directed into the plane of the figure. Determine the direction (clockwise or counterclockwise) of the induced current in the loop when (a) $B$ is increasing; (b) $B$ is decreasing; (c) $B$ is constant with a value of $B_{0}$ . Explain your reasoning.

a. If the magnetic field is increasing and is into the page, the induced magnetic field must oppose that change and point opposite to the external field's direction, thus creating a counterclockwise current in the loop.b. If the magnetic field is decreasing and is into the page, the induced magnetic field must oppose that change and point in the external field's direction, thus resulting in a clockwise current in the loop.c. If the magnetic field is constant, there is no changing flux, and therefore no induced current in the loop.

Physics 102 Electricity and Magnetism

Chapter 21

Electromagnetic Induction

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Magnetic Field and Magnetic Forces

Sources of Magnetic field

Inductance

Alternating Current

University of Michigan - Ann Arbor

University of Washington

Hope College

McMaster University

Lectures

03:27

Electromagnetic induction is the production of an electromotive force (emf) across a conductor due to its dynamic interaction with a magnetic field. Michael Faraday is generally credited with the discovery of electromagnetic induction in 1831.

08:42

In physics, a magnetic field is a vector field that describes the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude (or strength); as such it is a vector field. The term is used for two distinct but closely related fields denoted by the symbols B and H, where H is measured in units of amperes per meter (usually in the cgs system of units) and B is measured in teslas (SI units).

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A circular loop of wire is…

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Q1. A circular loop of wir…

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for this problem, we have a circular loop in a magnetic field. Our goal is to find the direction of the induced current based on different situations the Byfield. So whether that's increasing, decreasing or remaining the same on this diagram, I've depicted R B field going into the page, and that's drawn with little X marks. So this problem is gonna be an exercise in Monday's law. And one version of London's law states that the induced Byfield is established and mitigate the change in the Met magnetic flux. So let's write that down here. The induced be field is established to mitigate the change in net magnetic clocks. So if we determine what that induced the field is the orientation of that, we can easily find the direction of the induced current from our right hand roll. Let's start out with part A, and I'm gonna code this green because on our diagram, I'm gonna draw green for the be induced field. So here we have our external Byfield is increasing. If that external field is increasing, we have a larger magnitude into the page. To mitigate that change we need are induced field to point out of the page. So drawing that on a diagram out of the pages depicted by this little green circle and a dot in the middle cha largest emphasize here out of age and in order to find the direction of the Indies current. With this, we call on our right hand roll, which says Wrap your four fingers around the be vector are induced. Be vector so that your thumb is pointing in the direction of the arrow. And the way that your direct the way that your forefingers are curling gives us the direction of our current. So in here we have that current being counterclockwise counter clock, eyes induced kind for the next part code. This in orange we have our external Byfield is decreasing, decreasing. So if that's decreasing, we know that the magnitude into the page is getting smaller and value. So to mitigate that change we need are induced field to be pointing into the page. So here that is into the page and same right hand rule. Here thio, figure out the direction of the current point your thumb in the direction of your be vector, your induced defector and the way that your fingers curl around that vector gives you the direction of your induced currents. So here we have a clockwise current clockwise induced Chris and Lassie. We have be remains constant, constant, be not will for external field. Our external B is remaining constant. We have no net change of flux if there's no change in the flux. There's no induced field that's established and with no induced field that we get no induced current, so you get no induced QWERTY.

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