Insights Symmetry Arguments and the Infinite Wire with a Current

[Orodruin]

Many people reading this will be familiar with symmetry arguments related to the use of Gauss law. Finding the electric field around a spherically symmetric charge distribution or around an infinite wire carrying a charge per unit length are standard examples. This Insight explores similar arguments for the magnetic field around an infinite wire carrying a constant current $I$, which may not be as familiar. In particular, our focus is on the arguments that can be used to conclude that the magnetic field cannot have a component in the radial direction or in the direction of the wire itself.
Transformation properties of vectors
To use symmetry arguments we first need to establish how the magnetic field transforms under different spatial transformations. How it transforms under rotations and reflections will be of particular interest. The magnetic field is described by a vector $\vec B$ with both...

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