A closely wound rectangular coil of 80 turns has dimen-sions of 25.0 cm by 40.0 cm. The plane of the coil is rotated from a position where it makes an angle of 37.0° with a magnetic field of 1.70 T to a position perpendicular to the field. The rotation takes 0.0600 s. What is the average emf induced in the coil?

Video transcript

Hi everyone today we are going to actually calculate the mean or the average in use E M F. And 100 turned circular coil with a radius of 30 centimeter which is placed in a uniform 2.1 Tesla magnetic field where the orientation of the coils plane relative to the magnetic field itself is going to be changed from 35 to 85 degrees in 0.80 point 08 seconds. Okay, so first we want to identify all the necessary information given in this particular problem statement. So first we have the number of turns or N. Which is going to be 100 and we have the radius of 30 centimeters Which will correspond to 0.3 m. And then the magnetic field we have is going to be 2. Tesla. And the orientation is going to be changed from 35 to 85. I'm gonna write down the file five I Is going to be 35° while five F. or final is going to be 85°. Okay, so next we have the amount of time where it changed its rotation or its orientation And that will just be the Delta T. Which is going to be 0.08 seconds. Okay, those are all our known information in this problem statement. So next we want to recall that rotating the coil changes the angle between the coil and the magnetic field which will actually change the magnetic flux to everything. So, because there's a change in magnetic flux recall that induced E M F. Can only happen when there's a change in magnetic flux. So since there's a change then there's also going to be an induced E M F within the coil. So here are five is going to be the angle between the coil and the magnetic field B With the initial orientation of 35 and the final orientation of 85. So next um we can actually use this formula to calculate the average or mean induce E. M. F in the coil. So E M F is just epsilon here. So absalon F. Or mean E M F is going to be calculated by n. Multiplied by A B. Multiplied by A. So the number of turns multiplied by the magnetic field, multiplied by the area, multiplied by the absolute value of cosine of the final minus cosign of initial orientation. Just like so, and we have to define this by data. T to find the average. So this is the formula that we're going to be using. If you can tell we have all the necessary for information here except for the A. So I'm just going to calculate the real quick. The area of the coil is going to be just normal pi r squared. So the hour is going to be 0.3 m. So this is going to then be 0. m squared. Okay, so now we can actually start calculating the E M F average or mean E M F. So we have the end of 100. We have the B. Of 2.1 Tesla. We have the A. That we just found 0.2827 m squared. Multiplied by the absolute value of cosine 85° - Coastline. 35 Divided by the Delta T. Value, which is 0.08 seconds. Okay, so this is all the necessary information needed So we can solve and plug this into our calculator to gain average E. M. F. Or mean in use E. M. F. In the coil of 43.46 fault. So this is going to be the answer to our problem and that will correspond to option C. Here in the answer choices. And that will be all for this particular practice problem. If you can still have a little bit confusion on this particular topic, make sure to check out our other lesson videos similar to this one. To gain a better understanding of this topic. And that will be all for this one. And thank you