In a physics laboratory experiment, a coil with 200 turns enclosing an area of 12 cm^2 is rotated in 0.040 s from a position where its plane is perpendicular to the earth's magnetic field to a position where its plane is parallel to the field. The earth's magnetic field at the lab location is 6.0*10-5 T. (b) What is the average emf induced in the coil?

Video transcript

Hi, everyone. In this particular practice problem, we are asked to actually determine the mean E M F induced in the coil where we will have a coil with an area of 15.6 centimeters squared made out of 300 turns off a conducting wire And the coil will rotate so that the orientation of the coil with respect to the Earth's magnetic field will change from parallel to perpendicular. And the Earth's magnetic field at the coils location will equal to 4.7 times standard of power of -5 Tesla. And the time required for the rotation is 0.8 seconds. And we would like to determine the mean E M F induced in the coil. And the options are 0.31 Meli fold, 0.27 milli fold, 0.21 milli fold and 0.36 Meli fold. So in order for us to actually uh solve this problem and find the mean E M F induced in the coil, we wanna recall that um induced E M F is given as the absolute value of epsilon or induced ems is going to equals to N multiplied by the absolute value of the change in the magnetic flux or five B over time. So the N in this case is going to be the number of turns, the five B is just the magnetic flux passing through each turn of the coil and the delta T is over time. Also, we want to recall that the magnetic flux here P five B can be calculated by multiplying B multiply it by a multiply it by a cosine of five where B is the magnetic field, A is the area and phi is the orientation angle. In this case, the orientation angle changes from phi I or um initial phi equals zero degrees and phi F initial or final orientation 90 degrees which is just a change from parallel to perpendicular. So as the coil rotates, we want to determine the average E M F. And in order to do that, then the formula for the average E M F which is derived from our normal um E M induced E M F formula will then become um and multiplied by the magnetic flux initial minus N multiplied by the magnetic flux final over the amount of time which is delta T um in absolute value. So the delta T is given in the problem statement which is 0. seconds. OK. So uh basing it off of this formula right here, we have to calculate the total initial flux and the total final flux in order for us to actually determine the um average and use E M F. So let's start with the total initial flux. So the total initial flux is actually going to be N multiplied by five I which will be N multiplied by. Um we want to substitute this um magnetic flux formula into this five I. But change the uh five value here into um the P five I value which is zero degrees. So this is going to be B multiplied by a multiplied by cosine of uh P P I. And that will be 300 multiplied by the B is the earth's magnetic field which is 4.7 times 10 to the power of minus five tesla at the point of the coil. And the area is the 15. times 10 to the power of minus four m squared because 15.6 is in centimeters squared. And this will be multiplied by cosine of zero degrees. And then the result of this will be actually and multiplied by five I come out to be 2.1 times 10 to the power of -5 Weber or WB. So that is the total initial flux. And now we want to also find the total final flux in order for us to actually determine the induced uh average in U E M F. So similarly to the total initial flux, the total final flux is just N multiplied by P five F and that will be N multiplied by B multiplied by a multiplied by cosine of P five F. And that will be 300 multiplied by a 4.7 times 10 to the power minus five tesla. All of this and B and A are pretty much the same. The only difference are going, the only difference is just going to be on the orientation angle Which is going to be a cosine of 90°. And if we want to recall the cosine of 90° is actually zero so the total final flux here is going to actually equals to zero Weber. OK. So now that we have the total initial and total final flux, we can actually calculate the average in use E M F which is I'm gonna um rewrite our formula here which is the total initial flux minus total final flux over the amount of uh time that it takes for it to rotate or change its orientation. And this will actually come out to be 2.1 times 10 to the power of minus five Weber divided by the delta T or minus zero, divided by delta T which is 0.8 seconds given from the problem statement. And this will actually come out to be 0.27 times 10 to the power of minus three fault. And in millivolt, the average induced E M F is going to actually be 0.27 times that uh 0.27 mili fold. So the answer to this particular practice problem is going to be 0. M4, which will equal to option B. So option B with an average in use or mean EMF in use in the coil of 0.27 is going to be the answer to this practice problem. And that'll be all for this particular uh video. If you guys have any sort of confusion, please make sure to check out our other lesson videos on similar topics and that'll be it. Thank you.