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A rectangular circuit is moved at a constant velocity of 3.0 $\mathrm{m} / \mathrm{s}$ into, through, and then out of a uniform 1.25 T magnetic field, as shown in Figure $21.65 .$ The magnetic field region is considerably wider than 50.0 $\mathrm{cm} .$ Find the magnitude and direction (clockwise or counterclockwise) of the current induced in the circuit as it is (a) going into the magnetic field, (b) totally within the magnetic field, but still moving, and (c) moving out of the field. (d) Sketch a graph of the current in this circuit as a function of time, including the preceding three cases.

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a. 0.225 $\mathrm{A}$b, $I=0$c. $\mathrm{I}=0.225 \mathrm{A}$

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

University of Sheffield

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 rectangular circuit is m…

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Arectangular circuit is mo…

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A rectangular 10.0 $\mathr…

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As shown in the figure, a …

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A rectangular $10.0 \mathr…

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A magnetic field passes th…

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Figure $30-72 a$ shows a r…

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A current is set up in a w…

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Figure $32-30$ shows a cir…

so we can actually draw what this circuit looks like. So here we have a resistance of 12.5 arms. Ah, here we have, eh? Velocity of 3.0 meters per second. Ah, this length down here is 50 centimeters and then this length on the side of 70 centimeters and then going inside the inside the page is ah, a magnetic field 1.5 to 1.25 Tesla's rather. So this would be the complete circuit. Um, we know that, um when the loop is totally within the field, the flux through the loop is not changing and there is no induced imf. So at that point, you can say that the induced current has a magnitude of eye equaling the IMF, divided by four weaken Get the direction from the lens law. So for party Ah, we have going no going into the magnetic field. So for going into the magnetic field, eye's going to be equal. Tio Ah, either what about our? And so I will be equal to be the the part about our and this will be a 1.25 test lis times 0.750 meters times three meters per second and then divided by the resistance of 12.5 arms. And we find that either current is going to be equal to 0.225 amps now to find the direction means that they use a lens law. We know that the magnetic flux through loop is out of Paige and increasing. So if it's out of page increasing, that means that the magnetic fields we can say that the magnetic field is into the page. And if the magnetic fields into the page again inside the loop, the induced current is clockwise, so this would be the direction and this would be the magnitude of the current for part B. We know that here the flux isn't changing. It's moving with the magnetic field, so the flux is not changing. So the induced E. M s and the induced current are zero. They have new no magnitude on. And this is again only because it is moving with the magnetic fields now apart. See, apart party. We're going into the magnetic field here. Of course, we're going to be moving out of the magnetic field so we can say that I was going to be equal to IMF over our This is going to be simply 0.225 amps. Now, at this point, we can say lets my apologies, it's we do this point 2 to 5 amps. Now, at this point, we know that the flux through the loop is out of the page inside loop. Given this, we knew that the magnetic field must be into the page, which means that the induced current must be counterclockwise, So this would be the direction and this would be the magnitude of the current. Now, for part D. They're asking us for a quick Ah, Graff s o on the X axis will have time, seconds, and then the why will have the current and amps. So essentially, it will be like this where we can say that this is going to be time of a time of B. This is when it was moving with the magnetic field. This is moving away from the magnetic field, and then this is moving eyes moving into going into the magnetic field. So this would be the full diagram of both of the three cases we just explained through math. This is explaining it essentially graphically, so that would be the end of the solution. Thank you for watching

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