Determining Direction of Magnetic Force on a Moving Bar Magnet Near a Wire Loop

[nickr96]

Homework Statement

A bar magnetic is moved along the axis of a circular wire loop. In the figure below, (A) and (C) show the bar magnet moving toward the wire loop, while (B) and (D) show the bar magnet moving away from the wire loop.
Image: https://gyazo.com/2944a79393e7955214b281da58e7b0b8
Trying to determine in which cases the direction of magnetic force on the bar magnent is up and in which cases it is down.

Homework Equations

Not trying to determine any actual values, just direction.

The Attempt at a Solution

I've already determined that in cases B and C the induced current in the wire is clockwise and in cases A and D the induced current in the wire is counterclockwise. However I'm unsure as to how to use this information in the correct way to determine the direction of magnetic force acting on the bar magnet. It almost certainly has to do with the right-hand rule, given that I know both the direction of the induced current and magnetic field in the loop. However, because it is a loop of wire in cases A and D the magnetic field is flowing "up" inside and loop and "down" outside the loop, and vice versa for cases B and C. As such, I'm unsure what the direction of the magnetic field should be when trying to utilize the right-hand rule.

 

[TSny]

The Attempt at a Solution

I've already determined that in cases B and C the induced current in the wire is clockwise and in cases A and D the induced current in the wire is counterclockwise.

OK, sounds good.

However I'm unsure as to how to use this information in the correct way to determine the direction of magnetic force acting on the bar magnet. It almost certainly has to do with the right-hand rule, given that I know both the direction of the induced current and magnetic field in the loop. However, because it is a loop of wire in cases A and D the magnetic field is flowing "up" inside and loop and "down" outside the loop, and vice versa for cases B and C. As such, I'm unsure what the direction of the magnetic field should be when trying to utilize the right-hand rule.

What's important is the loop's magnetic field at the location of the bar magnet. Imagine a bar magnet placed above the loop shown here:
http://ipodphysics.com/magnets-loop-or-coil.php
If the magnet is oriented as in case (A) in your problem, can you see what direction the force on the magnet would be?

 

[nickr96]

OK, sounds good.

What's important is the loop's magnetic field at the location of the bar magnet. Imagine a bar magnet placed above the loop shown here:
http://ipodphysics.com/magnets-loop-or-coil.php
If the magnet is oriented as in case (A) in your problem, can you see what direction the force on the magnet would be?

Okay, so I'm unsure of how the magnetic field produced by the magnet and the magnetic field produced by the induced current interact. Is this actually simply a problem of repulsion and attraction? In the picture you linked, the induced magnetic field is the same as in case A, so if you were moving the north end of the magnet down towards the loop, it's akin to moving the north ends of two magnets together, in which case they'd repel and for the case of the loop the magnet would be repelled from the loop, indicating an "upward" direction of motion in relation to the loop. Is this the correct way of thinking about the problem?

 

[TSny]

Is this actually simply a problem of repulsion and attraction? In the picture you linked, the induced magnetic field is the same as in case A, so if you were moving the north end of the magnet down towards the loop, it's akin to moving the north ends of two magnets together, in which case they'd repel and for the case of the loop the magnet would be repelled from the loop, indicating an "upward" direction of motion in relation to the loop. Is this the correct way of thinking about the problem?

Yes, that's a good way to think about it.

Another way is to realize that a N-pole of a magnet always feels a magnetic force in the direction of the B field that the N-pole is placed in. Since the loop's magnetic field is upward at the location of the N-pole, the N-pole will experience an upward force. Of course, the S-pole of the magnet will feel a force opposite to the direction of the loop's field. So, the S-pole of the magnet will feel a force downward at the same time that the N-pole feels a force upward. But the force on the N-pole is stronger than the force on the S-pole because the S-pole is farther from the loop (where the loop's field is weaker). So the net force on the magnet is upward. Whew!

You might prefer to stick with your way. But it's good practice to see it in different ways.

 

[nickr96]

Yes, that's a good way to think about it.

Another way is to realize that a N-pole of a magnet always feels a magnetic force in the direction of the B field that the N-pole is placed in. Since the loop's magnetic field is upward at the location of the N-pole, the N-pole will experience an upward force. Of course, the S-pole of the magnet will feel a force opposite to the direction of the loop's field. So, the S-pole of the magnet will feel a force downward at the same time that the N-pole feels a force upward. But the force on the N-pole is stronger than the force on the S-pole because the S-pole is farther from the loop (where the loop's field is weaker). So the net force on the magnet is upward. Whew!

You might prefer to stick with your way. But it's good practice to see it in different ways.

Thanks for your help!