# Charged particle flying into an electric field

1. May 5, 2010

If a proton flies into a magnetic field I've seen the trajectory but I'm not sure about the directions of all the forces involved. In this picture
[PLAIN]http://img7.imageshack.us/img7/7065/helicinbfld.jpg [Broken]
I drew in a red, blue and yellow arrow. I assume the proton is moving in the direction the red arrow which is along the magnetic field lines but I have no idea what direction it was travelling before it entered the magnetic field. Was it travelling in the direction of the yellow arrow before entering the magnetic field then once it entered got stuck in that helicoidal trajectory because of the force exerted by the magnetic field?

Those green lines I assume are the magnetic field lines. If so why is the proton travelling in their direction?

Last edited by a moderator: May 4, 2017
2. May 5, 2010

### Born2bwire

The magnetic field induces a force on the proton that is equal to
$$\mathbf{F} = q\mathbf{v}\times\mathbf{B}$$
Assume that the B field is along the z direction and we can rotate our coordinate system so that the proton has a velocity with only x and z components. Looking only at the force due to the v_x component, you will find that the magnetic field's force causes the charge to move in a circular orbit. This is because the force changes so that it is always normal to the direction of the velocity in the x-y plane (since B is oriented along the z-axis). The radius of this orbit is dependent upon the charge strength, charge's mass, charge's velocity, and the strength of the magnetic field. The force due to the v_z component is zero as this velocity is directed along the direction of the magnetic field. Thus, the result is that the proton moves in a corkscrew motion.