The armature of a small generator consists of a flat, square coil with 120 turns and sides with a length of 1.60 cm. The coil rotates in a magnetic field of 0.0750 T. What is the angular speed of the coil if the maximum emf produced is 24.0 mV?

Video transcript

Everyone in this particular example we are asked to calculate the angular speed of the coil where a circular coil with a radius of 1. cm having won 50 turns rotates in a magnetic field of 0.0650 T. or Tesla. If the maximum EMF produced is 28 million fold. Okay, so first what we want to do is to identify every single um given information that we have here. So first what we have is the actual radius itself. So r is going to be 1.80 centimeters or essentially 1.80 times 10 to the power of minus two m. Remember we wanted to be an asset units and then we have 1 50 turns which is going to be in our end value here And we have the actual strength of the or magnitude of the magnetic field itself which is going to be B which is 0.0650 Tesla. T. And we have last E M F. Maximum E M F. Produced which is going to be e max and this is going to be 28 million volt or 28 time stand to the power of minus three fold. Just like that. Okay, so next we want to actually recall what kind of formula needed for this particular problem. So recall that imax can actually be calculated by multiplying the number of terms multiplied by the magnetic field, multiplied by the area, then multiplied by the W or the omega or the angler speed off the coil itself. So from this formula and what is actually given, we can actually start solving. But first I guess to make it easier for us to solve for a we want to calculate what the area is using this radius. So A is going to be pie are using the formula of pi r squared and is then going to be pi multiplied by 1.80 times 10 to the power of minus two m squared. And therefore A is going to then actually be 0.102 m squared. Okay, so now we can actually substitute everything or all of our known information into this formula here to find what W is. So imax is going to be 28 times 10 to the power of minus three fold equals 1 50 is n. And then the B is going to be 0. and then the area is the one that we just find and the omega is the one that we want to found here. Okay, so after doing some rearrangements, we know that the omega here is going to then be 28 times 10 to the power of minus three fold divided by all of this. Everything on this side, 1 50 0.65. Tesla 0.12 m quick. Okay, so the omega is then going to actually be 22.82 rat per second And that will actually be the answer to this problem, 2.8 to write per second, which will correspond to option C. That we have in the option here, option C. And that will be it for this particular practice problem. If you can still have any sort of confusion, please make sure to check out our other lesson videos regarding this topic, and that will be all for this problem. Thank you.