Accelerating electromagnetic system

BruceW

The current in the wire creates a magnetic field. This magnetic field causes a force on the magnet.

If you imagine the magnetic field lines from the wire and the magnetic field lines from the magnet, you can see what direction is the force on the wire and on the magnet. (a general quick and easy rule of thumb is that the magnetic field lines like to be as uniform as possible).

BruceW

for example, on the lower part of your picture, the current is going into the page, so in the space just above the 'north' pole, the magnetic field lines from the magnet are going against the field lines created by the wire. And in the space just below the north pole, the field lines are almost matching up. Therefore, this magnet will be pushed downwards, so that the field lines will become less steeply curved.

BruceW

Another way to work it out is if we give our magnets a specific form. For example, the magnets might be made of solenoids. In this case, you can work out the Lorentz force on the charged particles in the wire of the solenoid, and you can work out the force on the 'magnet' (i.e. solenoid), which gives the same answer as the other method.

DynastyV

I took a look at your solenoid example and found that all the forces on the solenoids cancel out. Here is a picture of the top part of the loop. A similar picture can be drawn for the bottom part of the loop.



Edit: The effect is similar to a compass needle aligning with Earth's magnetic field

BruceW

The green arrows (the force on the wire) is almost horizontal, but not. Because the wire is not exactly horizontal to the central wire, all the green arrows will be pointing downward slightly. This is the force on the magnets.