33.1:
Electromagnetic Waves
Consider a static electric charge. It creates a stationary electric field around it. When the charge starts moving, a magnetic field is additionally produced orthogonal to the direction of the moving charge.
If a moving charge accelerates by oscillating about a point, the electric field around it also starts oscillating.
According to Ampere-Maxwell's law, this time-varying electric field produces a displacement current, which induces another time-varying magnetic field perpendicular to the electric field.
From Faraday's law, a time-varying magnetic field, in turn, produces an electric field, and this process continues.
The sequential induction of both fields results in self-sustaining electric and magnetic fields in regions farther away from where they originated.
These fields propagate through space, creating electromagnetic waves that do not require a medium to sustain this motion.
The electromagnetic waves produced have the same frequency as the oscillation frequency of the accelerated electric charge.
These waves are transverse, as the constituent electric and magnetic fields oscillate perpendicular to and in phase with each other and are also perpendicular to the direction of propagation.
33.1:
Electromagnetic Waves
James Clerk Maxwell formulated a single theory combining all the electric and magnetic effects scientists knew during that time, calling the phenomena his theory predicted “Electromagnetic waves”. He brought together all the work that had been done by brilliant physicists such as Oersted, Coulomb, Gauss, and Faraday and added his own insights to develop the overarching theory of electromagnetism. Maxwell’s equations, combined with the Lorentz force law, encompass all the laws of electricity and magnetism. However, the symmetry that Maxwell introduced into his mathematical framework may not be immediately apparent; Faraday’s law describes how changing magnetic fields produce electric fields. The displacement current introduced by Maxwell instead results from a changing electric field and accounts for a changing electric field producing a magnetic field. The equations for the effects of both changing electric fields and changing magnetic fields differ in form only where the absence of magnetic monopoles leads to missing terms. This symmetry between the effects of changing magnetic and electric fields is essential in explaining the nature of electromagnetic waves.
To see how the symmetry introduced by Maxwell accounts for the existence of combined electric and magnetic waves that propagate through space, imagine a time-varying magnetic field produced by a high-frequency alternating current. From Faraday’s law, the changing magnetic field through a surface induces a time-varying electric field at the boundary of that surface. The displacement current source for the electric field, like Faraday’s law source for the magnetic field, produces only closed loops of field lines, because of the mathematical symmetry involved in the equations for induced electric and induced magnetic fields. In turn, the changing electric field creates a magnetic field according to the modified Ampère’s law. This changing field induces another electric field, which in turn induces another magnetic field, and so on. We then have a self-continuing process that leads to the creation of time-varying electric and magnetic fields in regions farther and farther away from the point where they first originated. This process may be visualized as the propagation of an electromagnetic wave through space.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from 16.1 Maxwell’s Equations and Electromagnetic Waves – University Physics Volume 2 | OpenStax