[Physics Class Notes] on Electromagnetic Waves Pdf for Exam [2024]

The waves (or their photons, quanta) of the electromagnetic field, transmitting or radiating through space, transmitting electromagnetic radiant energy is the electromagnetic radiation. It consists of microwaves, radio waves, infrared, (visible) light, X-rays, ultraviolet and gamma rays. Naturally, EM radiation has electromagnetic waves, which are coordinated oscillations of electric and magnetic fields that transmit the speed of light, which, in a vacuum, is usually written as “c”. In standardized, isotropic media, the oscillations of the 2 fields are perpendicular to each other and perpendicular to the direction of energy and wave transmission, forming a transverse wave. The wavefront of electromagnetic waves produced from a point source (like a light bulb) is a sphere. The point of an electromagnetic wave within the electromagnetic band can be characterized by its frequency of oscillation.

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Electromagnetic waves of different frequency are termed by different names since they have different origin and effects on matter. In order of growing frequency and reducing wavelength these are microwaves, radio waves, visible light, ultraviolet radiation, infrared radiation, X-rays and gamma rays. EM waves are produced by electrically charged particles experiencing acceleration, and these waves can consequently interact with other charged particles, applying force on them. Electromagnetic waves carry energy, motion, and angular momentum away from their source particle and can impart those magnitudes to matter with which they interact. EM radiation is related with those electromagnetic waves that are free to transmit themselves (“radiate”) without the permanent influence of the moving charges that created them because they have attained sufficient distance from those charges. Therefore, Electromagnetic radiation is sometimes referred to as the far field. That means the near field denotes to EM fields close to the charges and current that directly created electromagnetic induction and electrostatic induction occurrences precisely.

How are Electromagnetic waves formed?

• Usually, an electric field is formed by a charged particle. A force is applied by this electric field on other charged particles. Positive charges speed up in the direction of the field and negative charges speed up in a direction opposite to the direction of the field.
• The Magnetic field is created by a moving charged particle. A force is applied by this magnetic field on other moving particles. The energy on these charges is constantly perpendicular to the direction of their speed and therefore only changes the direction of the speed.
• So, the EM field is formed by an accelerating charged particle. Electromagnetic waves are nothing but electric and magnetic fields drifting through free space with the speed of light. A speeding charged particle is when the charged particle oscillates about a symmetry position. If the frequency of oscillation of the charged particle is f, then it yields an electromagnetic wave with frequency f. The wavelength “λ” of this wave is written as λ = c/f. Electromagnetic waves passing energy through space.
• Electromagnetic waves are exposed by a sinusoidal graph. It contains time-varying electric and magnetic fields which are perpendicular to each other and are also perpendicular to the direction of transmission of waves. Electromagnetic waves are diagonal in nature. The graph is as shown below:

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Mathematical Representation of Electromagnetic Wave:

• A plane EM wave traveling is in the form of x-direction

• B(x,t)=Bmaxcos(kx−ωt+Φ)

• E(x,t)=Emaxcos(kx−ωt+Φ)

• In the EM wave, E is the electric field vector and B is the magnetic field vector.

• Maxwell gave the basic idea of EM waves, while Hertz experimentally confirmed the presence of electromagnetic wave.

• The direction of propagation of the EM wave is assumed by vector cross product of the electric field and magnetic field. It is Written as:

E⃗ ×B⃗.

Properties

Electrodynamics is the study of electromagnetic radiation, and EM is the physical phenomenon related to the concept of electrodynamics. Electric and magnetic fields follow the properties of superposition. Therefore, a field due to any precise particle or time-varying magnetic or electric field donates to the fields present in the same space because of other causes. Further, as they are vector fields, all magnetic and electric field vectors combine together according to vector addition. For i
nstance, in optics two or more coherent light waves may interact and by destructive or constructive interference produce a resultant irradiance differing from the total of the component irradiances of the individual light waves.

Ever since light is an oscillation and it is not affected by migrating through magnetic fields or static electric in a linear medium like a vacuum. Still, in nonlinear media, such as certain crystals, interactions can happen between light and static electric and magnetic fields — these interactions contain the Kerr effect and the Faraday effect.

In refraction, a wave passing from one medium to another of different density changes its speed and direction upon arriving the new medium. The ratio of the refractive indices of the media regulates the degree of refraction.

Electromagnetic radiation shows both particle properties and waves properties at the same time. Both particle and wave characteristics have been established in several experiments. Wave properties are more seeming when electromagnetic radiation is calculated over comparatively large timescales and over large distances while particle characteristics are highly evident when measuring small timescales and distances. For instance, when EM radiation is absorbed by matter, particle-like characteristics will be more obvious when a certain number of photons in the cube of the related wavelength is much smaller than one. It is not too difficult to experimentally detect non-uniform deposition of energy when the light is absorbed; still, this alone is not confirmation of “particulate” behavior. Rather, it reflects the significant nature of matter. Representing that the light itself is quantized, not just its interaction with matter is a more subtle affair.

Certain experiments show both the particle and wave natures of electromagnetic waves, like the self-interference of an individual photon. When a single or lone photon is passed through an interferometer, it passes through both paths, interfering with itself, as waves do, yet is noticed by a photomultiplier or other sensitive detector only once.

A quantum theory of the communication between EM radiation and matter such as electrons is defined by the theory of quantum electrodynamics.

Electromagnetic waves might be polarized, refracted, reflected, diffracted or interfered with each other.

Wave model

In standardized, isotropic media, electromagnetic radiation is a diagonal wave, meaning that its oscillations are perpendicular to the direction of energy transmission and travel. The magnetic and electric parts of the field stand in a stable ratio of strengths in order to satisfy the two Maxwell equations that state how one is created from the other. In a dissipationless (lossless) media, these B and E fields are also in point, with both failure minima and maxima at the same points in space. A simple misconception is that the B and E fields in electromagnetic radiation are out of point due to a change in one generates the other, and this could yield a phase difference between them as sinusoidal roles (as indeed occur in EM induction, and in the near-field close to antennas). Still, in the far-field electromagnetic radiation which is termed by the two source-free Maxwell curl operator a righter description is that a time-change in one kind of field is relative to a space-change in the other. These results need that the B and E fields in electromagnetic radiation are in-phase.

A vital aspect of light’s nature is its frequency. The frequency of a wave is the volume of oscillation and is calculated in Hertz, the SI unit of frequency, where 1 hertz = 1 oscillation per second. Light usually has multiple frequencies that sum up to form the resulting wave. Different frequencies endure different angles of refraction, a process known as dispersion.
A wave contains successive channels and crests, and the distance among two adjacent crests or channels is named the wavelength. Waves of the EM spectrum vary in size, from very lengthy radio waves the size of buildings to very small gamma rays minor than atom nuclei. Frequency is inversely proportional to wavelength. According to equation

V = f𝞴
In equation v is the velocity of the wave (c in a vacuum, or fewer in other media), λ is the wavelength and f is the frequency. As waves pass through boundaries among different media, their velocities change but their frequencies remain constant.

Electromagnetic Wave Equation:

• Electromagnetic wave equation explains the transmission of electromagnetic waves in a vacuum or over a medium.

• The EM wave equation is a second-order fractional differential equation.

• It is a 3-dimensional form of the wave equation.

• The standardized form of the equation is written as,

(υ2ph▽2−∂2∂t2)E=0

(υ2ph▽2−∂2∂t2)B=0

Given, υph=1μ
ϵ√

Electromagnetic Wave Intensity:

I=PA=12cϵ0E20=12cμ0B20

The velocity of Electromagnetic Waves in Free Space:

It is written by C=√1(μ0ϵ0)

Given,

μ0 is termed absolute permeability. Its value is 1.257×10−6TmA⁻¹

ϵ0 is termed absolute permittivity. Its value is 8.854×10−12C2N−1m⁻²

C is the velocity of light in vacuum = velocity of electromagnetic waves in free space = 3×108ms−1

Electromagnetic Spectrum:

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Electromagnetic waves are categorized on the basis of their frequency “f” or according to their wavelength λ=cf.

Wavelength ranges of different lights are as follows,

For visible light – around. 400 nm to approx. 700 nm
For violet light – about. 400 nm
For red light – about. 700 nm

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