Comments on the motion of magnetic field lines Available to Purchase

Belcher and Olbert recently showed that the concept of the motion of magnetic field lines can be helpful in teaching classical electromagnetism. Although this concept holds in many situations, it has important limitations. It is shown that the most common definition, $v=E×B∕B2$⁠, which is the one used by Belcher and Olbert, is not appropriate when an electrostatic field is present, unless the field satisfies special conditions. In an infinitely conducting medium where the electric field has no component parallel to the magnetic field, $E×B∕B2$ is still a meaningful definition of the motion of magnetic field lines (which follow the plasma motion as if “frozen-in”). It used to be assumed that space plasmas could be treated as infinitely conducting and therefore the concept of magnetic field line motion was used extensively. But local nonvanishing values of $E∙B$ can “cut” magnetic field lines and invalidate the frozen-in condition.