One of the important aspects of electromagnetism is understanding the patterns of the electric and magnetic fields that the charges and current produce. These patterns can often suggest a symmetry – a regular order to the pattern that helps us deal with the field. Symmetries are a deep part of physics. In this case, we are discussing geometric symmetries, which suggest that there's a particular kind of charge or current producing the field. These symmetries can be used to reformulate the calculations to find the electric field (Gauss' Law) or magnetic field (Ampere's Law) more simply.