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A $30.0 \mathrm{cm} \times 60.0 \mathrm{cm} \mathrm{rec}-$ tangular circuit containing a a 15$\Omega$ resistor is perpendicular to a uniform magnetic field that starts out at 2.65 $\mathrm{T}$ and steadily decreases at 0.25 $\mathrm{T} / \mathrm{s}$ . (See Figure $21.48 . )$ While this field is changing, what does the ammeter read?

3 $\mathrm{mA}$

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

Cornell University

University of Washington

Hope College

University of Winnipeg

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for this problem. We have a 30 centimeter by 60 centimetres circuit in the circuit. There's a 15 ohm resistor and a meter. The initial Byfield that this is in and the Byfield is perpendicular to the circuit starts out a 2.65 Tessa and it is decreasing in value at 0.25 Tests is per second. Our goal is to find the induced current and this would be what are a meter would read in this setting. So let's start off by writing what are induced current would be. So we know that our EMF is gonna be equal to our induce current multiplied by our resistance. So are induced current. It's gonna be r e m f divided by that resistance. We know the resistance. And now we have to find what are you in? That would be so miss setting Are Emma is gonna be the change in the flux through our circuit. Over the change in time, we can rewrite our flux as the Byfield multiplied by the area and these two are perpendicular. So we just have B times a no co sign the angle zero. So the cup sign is one provided. By our time, the area is not changing, so we can pull that out. That's gonna be our changing. Be over change in time and that's the information were given were told that this is decreasing at 0.25 Tessa's per second. So let's plug this in to our initial equation. So the induced current is that gonna be a over our and then multiple and by our change and be over our change in time. And we have all this information, so the area is 30 by 60 but that ended meters squared. Our resistance is 15 homes. And then we're told that our change in Byfield is 0.25 tests per second. Let's not worry about signs right now. Let's figure that out with Linda's Law. So 0.25 Tesla's per second. And if you plug off this in, we get 0.3 amps or three million amps. Now the Byfield on this depiction that I've drawn is into the page, so it's decreasing. That circuit wants toe set up its induced current to maintain ah, flux going into the page of that same value. So if the flux is decreasing into the page. The current wants to set up clockwise so that it's induced. Field is into the page, therefore mitigating the change in the overall flux.

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