Question

Prove that tge average energy density of the oscillating electric field

Answer 1

this point in the course we'll move into optics. This might seem like a separate topic from electricity and magnetism, but optics is really a sub-topic of electricity and magnetism. This is because optics deals with the behavior of light, and light is one example of an electromagnetic wave.

Light and other electromagnetic waves

Light is not the only example of an electromagnetic wave. Other electromagnetic waves include the microwaves you use to heat up leftovers for dinner, and the radio waves that are broadcast from radio stations. An electromagnetic wave can be created by accelerating charges; moving charges back and forth will produce oscillating electric and magnetic fields, and these travel at the speed of light. It would really be more accurate to call the speed "the speed of an electromagnetic wave", because light is just one example of an electromagnetic wave.

speed of light in vacuum: c = 3.00 x 108 m/s

As we'll go into later in the course when we get to relativity, c is the ultimate speed limit in the universe. Nothing can travel faster than light in a vacuum.

There is a wonderful connection between c, the speed of light in a vacuum, and the constants that appeared in the electricity and magnetism equations, the permittivity of free space and the permeability of free space. James Clerk Maxwell, who showed that all of electricity and magnetism could be boiled down to four basic equations, also worked ou

electromagnetic radiation (EM radiation or EMR) refers to the waves (or their quanta, photons) of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy.[1] It includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays.[2]

Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric and magnetic fields that propagate at the speed of light, which, in a vacuum, is commonly denoted c. In homogeneous, isotropic media, the oscillations of the two fields are perpendicular to each other and perpendicular to the direction of energy and wave propagation, forming a transverse wave. The wavefront of electromagnetic waves emitted from a point source (such as a light bulb) is a sphere. The position of an electromagnetic wave within the electromagnetic spectrumcan be characterized by either its frequency of oscillation or its wavelength. Electromagnetic waves of different frequency are called by different names since they have different sources and effects on matter. In order of increasing frequency and decreasing wavelength these are: radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays.[3]

Electromagnetic waves are emitted by electrically charged particles undergoing acceleration,[4][5] and these waves can subsequently interact with other charged particles, exerting force on them. EM waves carry energy, momentum and angular momentum away from their source particle and can impart those quantities to matterwith which they interact. Electromagnetic radiation is associated with those EM waves that are free to propagate themselves ("radiate") without the continuing influence of the moving charges that produced them, because they have achieved sufficient distance from those charges. Thus, EMR is sometimes referred to as the far field. In this language, the near field refers to EM fields near the charges and current that directly produced them specifically, electromagnetic induction and electrostatic inductionphenomena.