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. (a) What is the total magnetic flux through the coil before it is rotated? After it is rotated?

Question

Accepted Answer

Hey, everyone. So this problem is dealing with magnetic flux. Let's see what it's asking us. We have the axis of a circular coil that is rotated from 30 degrees to 70 degrees in 700.5 seconds. And that's in respect or with respect to the earth's magnetic field, the cross sectional area of the coil is 16 centimeters squared and the number of turns is 300. We're given earth's magnetic field value which is seven times 10 to the negative five teslas. And then we're asked to calculate the total magnetic flux through the coil initially when it's at degrees. And finally, when it's at 70 degrees, our answers will have both an initial and a final flux. And they are a 1.15 times 10 to the negative five and 2.12 point 91 times 10 to the negative five Wevers B 1.91 times 10 to the negative five and 2. times 10 to the negative five Wevers C 9.7 times 10 to the negative five and eight point sorry. And 3.83 times 10 to the negative five Wevers or D 2.91 times 10 to the negative five and 1.15 times 10 to the negative five letters. OK. So the first thing that we can recall here is that the magnetic flux through each turn is given by the equation Bye B which is paramagnetic flux is equal to B, the magnitude of our magnetic field multiplied by a cross sectional area multiplied by the cosine of data. And so we have B given to us in the problem, our cross sectional area was also given to us. And then our theta initially, we're going to have um degrees angle and then our final angle is going to be 70 degrees. And then our total flux is simply going to be N the number of terms multiplied by the flux through each term NBA go sign data. So initially, we have and no, I'm um magnitude of our magnetic field was given at seven times 10 to the negative five teslas multiplied it by our cross sectional area. And so that was given in the problem as 16 centimeter squared, we need to keep everything in standard units. So that's going to be 10, 16 times 10 to the negative four m squared multiplied by cosine of and sorry, we know N and N is 300. And so we can just plug all of that in and get our initial block and that is 2.91 times 10 to the negative five S. And we're going to do the same thing for our final total flux, the same equation. So it's going to be 300 turns seven times 10 to the negative fifth teslas multiplied by 16 times 10 to the negative four m squared. And now this time is cosine of the final beta which is 70 degrees. And so when we plug that in, we get a total final flux of 1.15 times 10 to the negative five letters. And so that is those two, I should say are the answer to this problem. We go back up to our multiple choice solutions. It aligns with answer choice D. So that's all we have for this one. We'll see you in the next video.

Verified Solution

Key Concepts

Magnetic Flux

Faraday's Law of Electromagnetic Induction

Area and Orientation of the Coil