Faraday's law to find direction of current

[Sheve]

Homework Statement

Using Faraday's law, state the direction of current in the loop on the left. (Picture attached)

Homework Equations

$$\epsilon$$ = -d$$\Phi$$/dt

The Attempt at a Solution

I know that, assuming the direction of the current on the right side of the loop is from positive to negative, the magnetic field induced by the current above the loop will go into the page, come out of the page in the center of the loop, and go into the page below the loop. However, once that loop starts rotating, I have a hard time keeping up, and I can't figure out which direction the current will lop in the other loop.

 

[vela]

Since you're looking for the current induced in the left loop, you need to first determine the direction of the magnetic field inside that loop. What you've found is that the field outside the right loop points into the page while the field inside the right loop points out of the page. Since the left loop is outside the right loop, the field points into the page inside the left loop.

Now, as the right loop begins to turn, does that increase or decrease the flux through the left loop? Once you know that, does the induced field need to augment or decrease the external field to oppose this change in flux? Then, finally, you can figure out which way the induced current must flow to create the induced field.

 

[Sheve]

Well, as the field begins to rotate, I believe the flux will decrease as the field becomes more parallel with the loop. Thus, the induced field must increase to augment the field and oppose the change in flux, which means the field going into the page will be strengthened, and right hand rule means that the current will flow clockwise in the left circuit. Thank you for your help!

 

[vela]

Yup, you got it!

 

[rwisz]

Based on Faraday's law, the direction of the induced current in the loop on the left will be counterclockwise. This is because the changing magnetic flux through the loop, caused by the rotating loop on the right, will create an induced electromotive force (EMF) that opposes the change in flux. This means that the induced current will flow in a direction that creates a magnetic field that opposes the changing magnetic field of the rotating loop. In this case, the induced current will create a magnetic field that goes into the page on the left side of the loop and out of the page on the right side, creating a counterclockwise current flow.