# Motion of charges

1. Jun 21, 2008

### Niles

1. The problem statement, all variables and given/known data
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?

2. Jun 21, 2008

### Hootenanny

Staff Emeritus
Oh but the charges are moving.

3. Jun 21, 2008

### Niles

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

4. Jun 21, 2008

### Hootenanny

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

5. Jun 21, 2008

### 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?

6. Jun 21, 2008

### Hootenanny

Staff Emeritus
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?

7. Jun 21, 2008

### Niles

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