Direction of Velocity and Force in a Moving Copper Bar in a Magnetic Field

[donjt81]

A copper bar has a constant velocity in the plane of the paper and perpendicular to a magnetic field pointed into the plane of the paper. If the top of the bar becomes positive relative to the bottom of the bar, what is the direction of the velocity ~v of the bar?

1. from right to left
2. from left to right
3. from bottom to top
4. from top to bottom

I am not sure what logic to use to approach something like this. Can someone help please?

 

[Doc Al]

Consider the electrons in the copper bar. Which direction must the magnetic force be on them if the top of the bar becomes positive? Then figure out what direction the bar must be moving so that the magnetic force is in that direction. (I assume you know how to find the magnetic force on a moving charge and the use of the right hand rule.)

 

[Astronuc]

Does the term "Lorentz force" sound familiar?

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html#c2

 

[donjt81]

So the electrons will move from the bottom of the copper bar towards the top so the force would have to be towards the left (using the right hand rule) So the force is to the left and B is into the sheet and then with the same right hand rule the copper bar will have to be moving from bottom to top.

does that sound right?

 

[Doc Al]

So the electrons will move from the bottom of the copper bar towards the top so the force would have to be towards the left (using the right hand rule)

Since you are told that the top of the bar becomes positive, the electrons must move towards the bottom. So the force on the electrons (which are negative) is downward.

 

[wazzup]

Hey... I had a question.. what are they referring to in the following?

" 1. from right to left
2. from left to right
3. from bottom to top
4. from top to bottom"

Do they mean when the bar is moving from right to left? bar moving from left to right? are the specifying the various directions of velocity?

Thanks

 

[Doc Al]

Do they mean when the bar is moving from right to left? bar moving from left to right? are the specifying the various directions of velocity?

Yes. They are asking you to specify the direction of motion of the bar that would explain the charge distribution.

 

[wazzup]

So do you use the third right hand rule? However, don't know the direction of the force. You specified it to be downward but doesn't that change with a different velocity direction?

 

[Doc Al]

Since it's the magnetic force that separates the charge, you do know the direction of that force: it's upward on positive charges and downward on negative charges.

As far as which right hand rule to follow, I can never keep track of all the variations. To me, there's only one right hand rule, which tells you how to find the direction of a cross product. The magnetic force is given by:
$$\vec{F} = q \vec{v} \times \vec{B}$$
so I use the right hand rule to tell me the direction of F given v and B. For more help on using the right hand rule, go to the hyperphysics link that Astronuc provided.

Since the direction of v isn't given--it's what you are trying to find--you may just have to try each possible direction of v until you hit the one that works. It only takes a few seconds to run through them all.

 

[donjt81]

so the bar will move left

 

[Doc Al]

Why do you say that? If the bar moves left, which way will the force be on a positive charge?