I am not much of a mathematician, and I am trying to understand Maxwell's equations. I am trying to visualise the structure of a magnetic field produced in a straight wire firstly by a DC current, and secondly by an AC current. I think I understand but I just need to make sure that I have understood correctly. Firstly, is it right to say that the magnetic field lines, produced by a DC current, exactly match the equipotential electric field contours. How I am visualising the electric field is that it is made up of many equipotential cylinders moving along with the current, whilst I am visualising the magnetic field as static, with its equipotential magnetic contours following the equipotential electric contours. Secondly, with an AC current the electric field around the wire is constantly accelerating up and down along its length. In this instance I am visualising the magnetic field as having the same circular structure, but this time instead of it being static it is rotating around its own axis, firstly in one direction and then in the other direction, as the current continuously changes direction. Am I right in the way that I visualise the structure and behaviour of these fields or have I misunderstood the equations?