Determining the direction of an induced current

[Vladi]

Homework Statement

In Fig. 32-4( a) there is a uniform magnetic field in the + x-direction, with a value of B = 0.20 T. The circular loop of wire is in the yz-plane. The loop has an area of 5.0 cm2 and rotates about line CD as axis. Point-A rotates toward positive x-values from the position shown. If the loop rotates through 50 ° from its indicated position, as shown in Fig. 32-4( b), in a time of 0.20 s, (a) what is the change in flux through the coil, (b) what is the average induced emf in it, and (c) does the induced current flow directly from A to C or C to A in the upper part of the coil?

Homework Equations

None are needed for this case if we are only dealing with question C.

The Attempt at a Solution

I am having trouble with question C. This is the logic that I followed before coming to my conclusion(current flows from C to A) . As the loop of wires rotates about CD, there is a change in magnetic flux. Because there is an increase of magnetic flux in the +x direction, the coil will oppose this by producing flux in the -x direction. By the right hand rule, I am able to determine that the induced current travels clockwise around the yz plane. Thumb points in the -x direction. Fingers curl around the x axis. Am I using the correct right hand rule? If not, how do I know which one to use? There is another one that I know of. The index finger is the velocity vector(the current), the middle finger is the magnetic field, and the thumb is the force vector. Any help is appreciated. [/B]

 

[NFuller]

Homework Equations

None are needed for this case.

You need the definition of flux and Faraday's law.

You should first calculate the flux as a function of the angle from the x-axis. Then use Faraday's law to find the induced emf. For the final part you can use Lenz's law.

 

[Vladi]

You need the definition of flux and Faraday's law.

You should first calculate the flux as a function of the angle from the x-axis. Then use Faraday's law to find the induced emf. For the final part you can use Lenz's law.

The change in flux of the coil is -3.6*10^-5 T*m. The average induced emf of the coil is 1.8*10^-4 Volts. Why would I needs the answers from part a and part b for part c? Don't mean to sound rude, but I stated that I'm only interested in part c.

 

[NFuller]

Sorry, I didn't realize that you already solved the first two parts.

The change in flux of the coil is -3.6*10^-5 T*m.

So if the change in flux is negative, the induced current will be such to resist this decrease. Using the right hand rule as you suggest, in what direction must the current be to produce this magnetic field?

 

[Vladi]

Sorry, I didn't realize that you already solved the first two parts.

So if the change in flux is negative, the induced current will be such to resist this decrease. Using the right hand rule as you suggest, in what direction must the current be to produce this magnetic field?

It's all good. You're just making sure that I'm following the standard format. I know that the magnetic field is directed in the +x direction. By Lenz's law, an induced emf always has such a direction as to oppose the change in magnetic flux that produced it. Thus, an induced magnetic field must be directed in the -x direction. If I point my thumb in the -x direction and curl my fingers, I get that the current flows from C to A, which is wrong according to my books key. This where I get confused. I know of two right hand rules. The index finger represents current, the middle finger represents a magnetic field, and the thumb represents a force vector. Do I use one for 2 dimensional problems and the other for 3 dimensional problems? Thank you for your time.

 

[NFuller]

Thus, an induced magnetic field must be directed in the -x direction

Not quite, its in the positive x direction. This is because the magnetic field in the coil is decreasing so coil wants to reconstruct the field, which points in the +x direction.

 

[Vladi]

Not quite, its in the positive x direction. This is because the magnetic field in the coil is decreasing so coil wants to reconstruct the field, which points in the +x direction.

Correct me if I'm wrong, but is this your logic: If the change in flux is negative, the magnetic field is getting weaker, so the coil will produce flux in the direction of the original magnetic field in order to reconstruct that magnetic field. If the change in flux is positive, the magnetic field is getting stronger, so the coil will produce flux in the opposite direction of the magnetic field in order to cancel the original field.

 

[NFuller]

I should have been more careful in my wording. The external field is constant but the flux is decreasing and the flux is the parameter that the coil is trying to preserve. If the coil creates a magnetic field in the +x direction this will help increase the flux back towards its original value.

 

[Vladi]

I should have been more careful in my wording. The external field is constant but the flux is decreasing and the flux is the parameter that the coil is trying to preserve. If the coil creates a magnetic field in the +x direction this will help increase the flux back towards its original value.

The flux increases whenever the coil generates a magnetic field in the direction of the original magnetic field. The flux decreases whenever the coil generates a magnetic field in the opposite direction of the magnetic field. By Lenz's law, the coil will always undo the change in flux. If I ever see that the change in flux is positive, the induced magnetic field better be directed at the opposite direction. If I ever see that the change in flux is negative, the induced magnetic field better be directed at the direction of the magnetic field.

 

[NFuller]

The flux increases whenever the coil generates a magnetic field in the direction of the original magnetic field. The flux decreases whenever the coil generates a magnetic field in the opposite direction of the magnetic field. By Lenz's law, the coil will always undo the change in flux. If I ever see that the change in flux is positive, the induced magnetic field better be directed at the opposite direction. If I ever see that the change in flux is negative, the induced magnetic field better be directed at the direction of the magnetic field.

Exactly!

 

[Vladi]

Exactly!

Thank you for all your help!