A square loop with a side length L=37.5 cm, a total...

A square loop with a side length L=37.5 cm, a total resistance R=12.0 ?, and N=125 turns of wire lies in the plane of the page. The loop is in a uniform magnetic field which points into the page, as shown in the diagram on the right. The strength of this magnetic field (B) increases at constant rate of $dB/dt$=0.500 T/s. (a) Use Faraday's law to find the magnitude of the current induced in the loop. Give your answer in units of Amperes (A). (b) Is the current flowing clockwise or counterclockwise? Explain your answer using Lenz's law.

Transcript

00:01 All right, greetings and salutations.

00:02 In this question we are given a loop of wire, a circular loop with a radius of 0 .0250 meters and a resistance of 0 .34 ohms, and it's inside of this magnetic field which is going into the page, and that is a time -dependent magnetic field given by 0 .320 t cubed.

00:20 I've dropped the units just for simplicity.

00:22 Everything's in si so we don't need to worry about it too much.

00:26 And we're told that initially there is zero teslas in the loop, so we're going to have an increasing into the page here.

00:33 And we're asked what is the current in the loop when the instant when b is equal to 1 .38 teslas.

00:40 So in order to do this we're going to go ahead and use faraday's law.

00:43 We know that our induced voltage is equal to our change in magnetic flux over our change in time, and we know that our change in magnetic flux is going to equal, well our change in our magnetic flux in this case is going to be b times a times n is equal to 1, cosine theta is equal to 1 because everything's nice and perpendicular.

01:00 So we're just going to have b times a.

01:02 I know that the area is not changing, that's a constant pi r squared, but i do know that b is changing, so i'm going to have some db dt here.

01:11 And then on the left -hand side i'm going to go ahead and say that my voltage or my induced potential is equal to i times my resistance.

01:19 That's just ohm's law there.

01:21 So my induced current is going to be negative pi r squared over my resistance r times db dt.

01:28 Well that's just the derivative of this function here.

01:30 So if i take the derivative of that i'm going to get 0 .960 t squared, and that will be db dt.

01:39 I know that's going to be positive.

01:41 And so i almost have everything, but i don't have what t is.

01:44 I was given, well the b field is 1 .38 teslas.

01:48 So i can say that my b field is 1 .38 teslas, and i know that my magnetic field equation is 0 .320 t cubed...

Question

Please give Ace some feedback