I have invented this little problem to help me understand the magnetic force better.
Imagine 3 positive charges all on a line. The first charge is separated by distance D from the second charge, and the second charge by distance D from the third charge. So
+ ---------------- + ------------------ +
The 3 charges are moving downwards at a constant velocity. The first and third charge have x axis positions which are permanently fixed - no force can change their minds. The middle charge is in perfect, peaceful free fall. For a long time the 3 charges have been moving in unison, downwards - the negative j-hat direction. The middle charge is in equilibrium between the electric repulsive forces due to the other two charges. It experiences no vertical forces, as it has constant vertical velocity.
Suddenly the 3 charges enter a B field. The magnetic field points into the page, so there is a magnetic force pointing towards the right on the middle charge. The other two charges don't matter.
What happens to the middle charge?
I am asking for the classical electromagnetism answer to the question, and in particular I am wondering:
By experiment it is so that there is the stated force on the magnetic field. But this force cannot do work. Therefore it should not be able to displace the charge in the direction of the 3rd, rightmost charge.
How can classical physics explain what's next? What exactly is happening here in terms of work? What principles underlie the hypothesis that the middle charge's vertical velocity falls, if that is the salient hypothesis?
I assume that there are no external forces acting on the system.
PS. obviously these charges have inertia - all equal (and gravitational fields sum to zero with electric at the middle charge).