Launching With Potential

Title: Launching With Potential

Artist: John Serlin

Quick Description: In our video, "How Easy Is It To Build An Electromagnet", we use an electromagnet and permanent magnet to create a launcher. This is an illistration of the magnetic field immediatley after launching the magnet.

More:

What Does This Show?

This is a solution to Maxwell's equations, which gives us the magnetic field. We assume the coil and the permanent magnet are both approximately magnetic dipoles.

Is this the only possible solution?

No at all! There are many possible valid solutions that would show correct magnetic fields. However in order to choose one of the many possible soltuions we made some assumptions:

Assumption 1:

No magnetic field may leave the box, this would be the same as placing everything inside a thick metal box where the magnetic field can't escape out of.

Assumption 2:

For simplicity we assume the launch is slow enough that we can ignore the displacement current term created by the induced EMF of the magnet moving. 

What do the colors represent?

Under normal circumstances the magnetic force is non-conservative, this makes calculating trajectories harder. Under these conditions the force experienced is depedent on the change over space of the dipole moment dottd with the magnetic field.  However given our particular circumstance the internal permanent magnet is restrained to slide within the tube. This means the magnetic dipole moment is constant. Then equation for force is dependent only on the gradient of a scalar function, this is a conservative potential. By this method we can see the magnetic field also as a conservative force field with points of high and low potential. As such this image is drawn with red representing high potential and blue representing low.