# Forces between parallel currents

• georgia

## 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?

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?