Comparison of Electric and Magnetic Forces

[godiva]

Homework Statement

Suppose that the instantaneous velocities of two positive point charges are parallel. Compare the electric and magnetic forces. Show that the ratio of the magnetic force (Fmag) to the electric force (Felec) is: Fmag/Felec = v1*v2/c^2
Where v1 and v2 are the velocities of particle 1 and particle 2 respectively, and c is the speed of light.

Homework Equations

F = qE + qv*B

The Attempt at a Solution

I know that you need to use the Lorentz force in some form, but I am confused as to how the speed of light is incorporated into the solution. This is a practice problem for my exam later on this week, so any help would be appreciated.

 

[collinsmark]

Hello godiva,

Welcome to Physics Forums!

I know that you need to use the Lorentz force in some form, but I am confused as to how the speed of light is incorporated into the solution. This is a practice problem for my exam later on this week, so any help would be appreciated.

The easy way is to first figure out what the magnetic field B is, caused by the first moving particle (charge q moving at a speed of v₁). Use the Biot-Savart law for a single particle. If you are using the general Biot-Savart law that is a function of current and wire length, substitute (current times length of wire) with (charge of particle times velocity of particle), which is the same thing for a single particle.

Once you know the magnetic field caused by the first particle, find the magnetic force on the second particle as it moves through the magnetic field with a velocity v₂.

Then take the ratio of magnetic force to the electric force.

Finally, note that $c = 1/\sqrt{\mu _0 \epsilon _0}$