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Homework Help: Electric and magnetic field between concentric, conducting cylinders

  1. Jun 2, 2014 #1
    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


    3. The attempt at a solution

    All I've managed is to say that there must be no net force, so
    I'm not sure how to work out the electric of magnetic field.
  2. jcsd
  3. Jun 2, 2014 #2
    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
  4. Jun 2, 2014 #3
    OK so using amperes law I get
    Is this right?
    And what's the relationship between electric field and potential difference?
  5. Jun 3, 2014 #4


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    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)
    [tex]\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}.[/tex]
    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.
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