A single loop of wire with an area of 0.0900 m^2 is in a uniform magnetic field that has an initial value of 3.80 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.190 T/s. (a) What emf is induced in this loop?

Video transcript

Hi, everyone. In this particular problem, we are asked to actually consider a rectangular coil with a varying magnetic field applied to the coil passes through the single loop. Single group has an area of 0.7 m squared. And the magnetic field is parallel to the coils access and decreases at a rate of 0.25 tesla per seconds were asked to actually find induce CMF if the magnetic field has an initial value of 2.7 tesla. So first, I'm going to start with creating a list of everything that's given. So we have the area To be 0.07 m square. We know that it's a single loop. So and equals to one or I'm just gonna ignore that here. And then we know that the magnetic field is parallel to the coils access. So that's essentially saying that our five or angle or data is zero degrees and it decreases at a rate of the magnetic field decreases at a rate of 0. tesla per second, which I'm going to write it down as D B over D T. And we have the initial value of the magnetic field of 2. tesla, we are asked to find the induced CMF and we want to recall that a change in the magnetic field or changing B actually is causing a change in the magnetic flux five B to the loop. And because there's a change in the flux, this induces an E M F in the loop as well. Because if we recall, we know that inducing MF can be calculated by just going to write down the absolute value of everything can be calculated by differentiating the magnetic flux over time with respect to time, which essentially also the magnetic flux itself can be calculated by multiplying the magnetic field times the area times the orientation angle or co sign tater or fi um just like so and in our particular case, right here we have a co sign of zero which is going to be one. So we can kind of neglect that part. So in this particular problem, we know that the A is constant while the B is changing. So we want to differentiate B with respect to T. So you want to pretty much substitute all this formula into this E M F formula here. So I'm just gonna do that real quick. So this side is going to be D of B multiplied by a multiplied by co sign of zero degrees, which is essentially equals to one over DT. And recall that the A is going to be constant. So the A can be out of the actual different shell here or derivative. So this is going to be a multiplied by D B over D T just like. So, and we know what A S we know A D B over D T is. So we can calculate the induced E M F. So A is going to be 0.7 m squared and the D B over D T 0.25 Tesla per second. So to induce E M F is then going to be 0.175 fault or essentially it will be option A just like. So, so that will be all for this particular problem. If you just have any sort of confusion, please make sure to check out our other lesson videos similar to this one and that will be all. Thank you.