Forces between parallel currents

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Homework Statement



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

Homework Equations



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

F= (μ0*I1*I2*l)/2πd

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?
 

Answers and Replies

  • #2
Hootenanny
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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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