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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

    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. 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
    B=μI/2πr
    Is this right?
    And what's the relationship between electric field and potential difference?
     
  5. Jun 3, 2014 #4

    vanhees71

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    Science Advisor
    2016 Award

    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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