30.11:
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.
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.
Suggested Reading
- Young, H.D. and Freedman, R.A. (2012). University Physics with Modern Physics. San Francisco, CA: Pearson; section 29.7; pages 978.
- Griffiths, David J. (1999). Introduction to Electrodynamics (3rd ed.). Upper Saddle River, New Jersey 07458; section 7.2.2; pages 305–306.