30.11: Electromagnetic Fields
Electric fields generated by static charges, often referred to as electrostatic fields, are characteristically different from electric fields created by time-varying magnetic fields. While the former is a conservative field, implying that no net work is done on a test charge if it goes around in a complete loop in the field, the latter is, by definition, not a conservative field; net work is done, and it is proportional to the rate of change of magnetic flux.
However, the observation of Gauss's law for electrostatic fields breaks down for fields generated by changing magnetic fields, because these always form closed loops. Thus, there is no net flux through a closed surface, as the number of field lines entering and leaving is the same.
Despite their differences, experiments reveal that they exert the same kind of force, the Lorentz force, on test charges. Moreover, these forces follow the principle of superposition. Consequently, the fields also follow the principle of superposition. Hence, they are vectorially added and simply called electric fields.
The distinction between conservative (electrostatic) and non-conservative electric fields is important only in specific cases, for example, inside an ideal inductor.
Nature fascinates us through its simplicity because it was not necessary for the fields produced by different mechanisms to exert the same kind of Lorentz force and add up vectorially. The same simplicity also applies to magnetic fields.
Steady currents produce magnetic fields that obey Ampère's law. However, changing electric fields also produce magnetic fields, in that the field exerts the same Lorentz force on a moving test charge and adds up vectorially with the field produced by steady currents. This observation justifies calling them both magnetic fields.
