Equation for the motion of an iron particle in a magnetic field

[ddddd28]

Hello,
Let's assume we put a small iron particle in a magnetic field. What is the equation of the route that the particle performs? Is it the minimal route length that is possible? (the magnet is a stick-form)

 

[rumborak]

It might look that way, but I don't think so.

As a general rule, the particle will experience an attraction in the direction of the biggest field density increase. That however means for example, if you place it right in the middle between the poles but above the bar, all it will do is go straight towards the middle of the bar. But, if you place it slightly say to the right of that point, the direction of attraction will sightly point towards to the right because the field lines also get more dense towards that direction.

So, in essence, slightly off-center the particle experiences a non-vertical force, which will make it hit the bar at an angle. That then obviously is not the direct route.

 

[ddddd28]

I wanted to know which mathematical equation describes the route