Magnetic Field Structure

SimonBennett

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?

Born2bwire

Ummm... Yeah, the magnetic field lines and electric field lines are both cylindrically symmetrical and they both fall off as 1/r. So the the field lines will be the same but they do not travel at all. It's a time invariant system and thus the fields remain stationary. It also should be noted that the direction of the fields along the lines are different. The magnetic field is oriented in the phi direction (along the length of the cylindrical lines) but the electric field is oriented in the rho direction (normal to the cylindrical lines).

As for AC current, then we excite electromagnetic waves. In the case of an infinite wire the waves spread out, in the far-field, as cylindrical waves. The amplitude and direction of the fields depends both on time and space but it is periodic in accordance with the frequency of the current. We do not really bother to think of field lines in this case due to the time dependency. Instead we just visualize the wavefronts, the surfaces of constant phase, and how they are arranged in space and move in time.

SimonBennett

Thanks very much for the reply. However, I am still not quite sure about the electric field around the wire. You say that this field is stationary, which I know it would appear to be as any measurements around the wire would yield the same results over time. However, the same could be said of a static electric field (if it were possible to set one up within the wire). However, in the case of the electric field emanating from the electric current this produces a magnetic field, whilst the electric field emanating from a static charge would not produce a magnetic field. Does this not mean that the electric field produced by the current is constantly moving along the wire, and that it only appears to be stationary due to its uniformity?