Do such field lines interact? Image two singular field lines rotated into alignment,
and then rotated out of alignment. There is no work done. However when in alignment the potential energy of the system of two field lines is maximum.
This increase in potential energy presents a energy barrier to field rotation. When the field lines are aligned.
\(U_{max}=2V_r\)
where \(r\) is the distance from the source of the field line to the meet point, \(s_{x,y,z}\) and, \(V_r\) the potential at \(s_{x,y,z}\) due to one source. When the field lines are not aligned,
\(U=0\)
since these are singular field lines and do not interact except at \(s_{x,y,z}\).
The energy barrier to field rotation is then \(U_{max}=2V_r\).
