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Forces between parallel currents

  1. Apr 5, 2007 #1
    1. The problem statement, all variables and given/known data

    Two narrow beams of electrons with velocities v and -v are injected into an evacuated chamber along the length l. Each beam moves with constant speed and carries a current I. The tendency for the beams to deflect each other through their mutual interaction is compensated by a magnetic flux density B perpendicular to the plane containing the two electron beams so that they travel in parallel straight lines a distance d apart (d << l). Show that the ratio f of the magnetic to the electric force on each of the beams due to their mutual interaction is vε0μ0

    2. Relevant equations

    For two parallel currents I1 and I2 the force on a length l of I2 is:

    F= (μ0*I1*I2*l)/2πd

    3. The attempt at a solution

    Using the above equation and substituting I1 = I and I2 = -I:

    F= -(μ0*I^2*l)/2πd

    I don't know what to do now, what is the electric force?

    All I know is Coloumb's law but I thought that only applied to static charges?
  2. jcsd
  3. Apr 5, 2007 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    Coloumb's law applies to all charges, stationary or not. However, in this case you need to consider the electric field of a finite line of charge. Have you met this before?
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