A circular loop of wire is in a region of spatially uniform mag-netic field, as shown in Fig. E29.15. The magnetic field is directed into the plane of the figure.

Determine the direction (clockwise or counterclock-wise) of the induced current in the loop when (a) B is increasing; (b) B is decreasing; (c) B is constant with value B_0. Explain your reasoning.

Video transcript

Hey everyone. So this problem is dealing with magnetic fields and induced current. Let's see what it's asking us. We need to determine the direction of current induced in a metal ring placed in a uniform magnetic field that is directed out the page for the following three cases. One where the magnetic field is increasing, two where the magnetic field is decreasing and three where the magnetic field is constant. So the first thing we can do here looking at this figure, we see the magnetic field be it's directed out of the page. And then we have this ring uh this me this metallic ring where we know that current is being induced from this magnetic field. So we can recall Lenz's law which states that the field of the current induced by a changing magnetic field is in the opposite direction of the magnetic field. So the field from the current is going to be in the opposite direction of the magnetic field. So for the first case, we have a magnetic field that is increasing, therefore, our flux is increasing. And so the field of the induced current is into the page. The magnetic field is increasing and it is out of the page. So the current is into the page, we can use our right handed grip rule to figure out the direction of current. So we put our thumb in the direction of the um current of the field of the induced current. So that's into the page and then the fingers curl in the direction that the current flows. So with your right hand thumb into the page, your fingers curl counter or sorry, your fingers curl clockwise. For the second scenario, we have a decreasing magnetic field. And so therefore, with the flux decreasing our magnetic field, sorry, the flux is going to be into the page. And so our induced current field is going to be out of the page. And so the right-handed rule when our thumb again is out of the page. Now our fingers are curling counter long lines. And then in the third scenario where our magnetic field is constant, again, we're calling Lenz's law where the current is induced by a change in magnetic field. If there is no change in magnetic field, there is no induced current. And so when we look at our multiple choice answers, this aligns with answer choice dean. So scenario one is clockwise. Scenario two is counterclockwise. And scenario three, we have no induced current. So that's all we have for this one, we'll see you in the next video