# Electric and magnetic field between concentric, conducting cylinders

1. Jun 2, 2014

### lar49

1. The problem statement, all variables and given/known data#
Two long, concentric, conducting cylinders of radii and b (a<b) each carry a current I in opposite directions and maintain a potential difference V.
An electron with velocity u (parallel to the cylinders) travels undeviated through the space between the two cylinders.
Find an expression for |u|

2. Relevant equations

F=q(E+u^B)

3. The attempt at a solution

All I've managed is to say that there must be no net force, so
E=-u^B
E=-|u||B|sinθ
I'm not sure how to work out the electric of magnetic field.

2. Jun 2, 2014

### dauto

Use Faraday's law to find the electric field and the relation between voltage and electric field to find the electric field.

EDIT: Sorry, I meant to say use Ampere's law to find the magnetic field

Last edited: Jun 2, 2014
3. Jun 2, 2014

### lar49

OK so using amperes law I get
B=μI/2πr
Is this right?
And what's the relationship between electric field and potential difference?

4. Jun 3, 2014

### vanhees71

Your magnetic field is right for the gap between the inner and outer cylinder (coax cable).

To answer your other question, you should think a bit. The equations are those for stationary fields, i.e., (in SI units)
$$\vec{\nabla} \times \vec{E}=0, \quad \vec{\nabla} \cdot \vec{E}=\rho, \quad \vec{\nabla} \cdot \vec{B}=0, \quad \vec{\nabla} \times \vec{B}=\mu \vec{j}, \quad \vec{j}=\sigma \vec{E}.$$
This holds in non-relativistic approximations for the movement of the electrons in the, and this is a damn good approximations for all household currents :-)).

In addition you need appropriate boundary conditions for the fields at the surfaces of the conductors. These you should find in any textbook of electrodynamics, e.g., Jackson, Classical electrodynamics.