Electromagnetic Fields

Recall Gauss's law for electric fields produced by charges and Faraday's law for electric fields created by the time-varying magnetic flux.

Since the former follows Gauss's law, its integral over a closed loop is zero; it is a conservative field. However, using Faraday's law, the latter is a non-conservative field.

Moreover, since it always forms a closed loop, its flux through any closed surface is zero. Thus, it disobeys Gauss's law.

Moving charges or steady currents produce magnetic fields which obey Ampère's law. However, time-varying electric flux gives rise to magnetic fields that do not obey Ampère's law.

Recall the aim of studying electromagnetism: calculate the force on a test charge so that, via Newton's second law of motion, its trajectory can be determined.

Experiments reveal that the conservative and non-conservative electric fields, and the Ampère's law obeying and disobeying magnetic fields, give rise to the same kind of Lorentz force on a test charge. Moreover, they are found to add vectorially.

Hence, they are added together and simply called electric and magnetic fields.