Motion of Charges: Surface Charge Density

[Niles]

Homework Statement

Let's take a look at an example: A surface charge s resides on a plate with area A. The plate is moving with a velocity v in a magnetic field B, so then the magnetic force on the plate will be:

$${\bf{F}} = \int {{\bf{K}} \times {\bf{B}}} \,d{\rm{a}}$$

where K is the surface charge density of the top plate.

How does it make sense to talk about a surface charge density in this case, when the charges themselves are not moving, but the plate is moving as a whole? Does this mean that the two scenarios equivalent?

 

[Hootenanny]

How does it make sense to talk about a surface charge density in this case, when the charges themselves are not moving, but the plate is moving as a whole? Does this mean that the two scenarios equivalent?

Oh but the charges are moving.

 

[Niles]

How can they be moving when the plane is finite and not part of a circuit?

 

[Hootenanny]

How can they be moving when the plane is finite and not part of a circuit?

Consider yourself standing inside a railway carriage that is traveling uniformally through a station. Are you moving?

 

[Niles]

Yes, I am.

But if that is the case, then wouldn't the charges constantly be in motion because of Earth's rotation and hence feel a magnetic force always in a magnetic field?

 

[Hootenanny]

But if that is the case, then wouldn't the charges constantly be in motion because of Earth's rotation and hence feel a magnetic force always in a magnetic field?

That depends. Suppose you introduce a magnet field by using a simple magnet, you place the magnet on a workbench and then place the plate on the bench next to the magnet. The plate is now in the magnetic field created by the magnet, but is the plate moving relative to the magnetic field?

 

[Niles]

Ahh, I see.. Very good, very good. Thanks!