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A coil of wire with 200 circular turns of radius 3.00 $\mathrm{cm}$ is in a uniform magnetic field along the axis of the coil. The coil has $R=40.0 \Omega$ . At what rate, in teslas per second, must the magnetic field be changing to induce a current of 0.150 $\mathrm{A}$ in the coil?

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

Rutgers, The State University of New Jersey

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this problem. We have a coil of 200 turns that has a radius of three centimeters and a resistance of 40 elms. There's a uniform Byfield along the axis of this coil and were asked to find what time rate of change in this Byfield would induce a current of 0.15 amps. So let's recall that this induced CMF CMF between the end points of this coil is given by the number of turns and multiplied by that change in the flux over the change in time. And our flux is just going to be our be field multiplied by our area, the B field and the perpendicular. The area are in the same direction, so we don't have to worry about the co sign or if we wanted to be explicit, that would be be a co sign that our co signing zero, which is one when we have a change in time. That area is not changing so we can pull that out. This is just gonna be r n wants played by r a over our d b those t. And so we see that Where don't that beat up the tea? What? We're trying to find Is this induced in math over the number of coils multiplied by the area. Now recall that the Duce, d and F it is also just gonna be the current won't planned by our resistance in the area. Since it's just a circular region, we have pie r squared. So putting that into here we have our Delta Bi don't The tea is equal to i r over and hi r squared and now we are given all of these specifications. So let's let's plug it in. We want our induced current to be your 0.15 Our resistance is 40 we have 200 turns and the radius is three centimeters and always put that into meters. Now if we plug all of that in where you get 10.6, Tesla's per second. So with this rate of change in the B field, we will get an induced current of 0.150 amps

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