Metal bar moving in a magnetic field

[darkar87]

Homework Statement

A metal bar with dimensions a,b,c is moving with constant velocity(V) in a magnetic field (B).Find the charge density in both of the ab sides.(B is constant)

Relevant Equations

F=qvB
F=Eq

When the bar moves ,magnetic force is applied to all the charged particles.At the equilibrium the electric and magnetic force have the same value and the positive and negative charges are accumulated in the two sides of ab.
Eq=qVB, E=VB
Here is when cannot continue,I thought it like a capacitor but the permeability is not given.
(sorry for my english)

 

[BvU]

Hello darkar, !

the permeability is not given.

No, but you can assume the Lorentz force opposes the potential from the charges huddled together on either end that repel each other. Think 'potential' !

[edit] and: it's a conductor, so: no E field inside the bar

 

[rude man]

Since the net E field in the bar is zero you know there are two equal and oppositely directed fields inside the bar. Call these Em and Es.
Es is the electrostatic field you are concerned with since it's the field beginning and ending on charges (the Em field is the source of the emf).

So, you know the emf and from what I've said you should be able to compute the Es field. This field will be the field at the two end faces. Knowing Es you know the surface charge density.

PS assume a vacuum or air so permittivity is $\epsilon_r = 1.0$.