# Magnetic Rotor

This example consists of a spinning dense circle within an initially stationary fluid. Within the circle, we set a uniform angular velocity up to a user defined radius. Periodic boundaries were used and this example was calculated up to a time of t=0.29, which corresponds to calculations found in the literature.

The initial conditions in the surrounding fluid are
$\rho=1, p=1, \textbf{B}=\left(\frac{2.5}{\sqrt{4\pi}},0,0\right).$
Inside the rotor, a higher pressure and an angular velocity is set
$\rho=10, v_a=1, r=0.1.$

The following images shows the density distribution and the magnetic field magnitude of a 5th order calculation on a 200×200 grid.

Plot of the density

Plot of the magnetic field