Electromagnetic Waves Revision Notes

Ruhul Amin Alig

A quick revision of all the important concepts

Electromagnetic Waves

Displacement Current
The current which comes into play m the region in which the electric field and the electric flux is changing with time. It is given by

I_{D} = ϵ_{o} \frac{d ϕ _{E}}{d t}

Physical behaviour of displacement current is same as that of induction current. Difference between Conduction current and Displacement current: For Static electric fields $I_{D} = 0$ . For time varying electric fields $I_{D} \neq = 0$

Conduction Current	Displacement Current
It arises due to the fixed charges.	It arises due to the change in electric field.

There can be some scenarios where there will be only conduction current and, in some case, there will be only displacement current.
Outside the capacitor there is only conduction current and no displacement current.
Inside the capacitor there is only displacement current and no conduction current.
But there can be some scenario where both conduction as well as displacement current is present i.e., $I = I_{C} + I_{D}$ .
Applying modified Ampere-Maxwell law to calculate magnetic field at the same point of the capacitor considering different ampere loop, the result will be same.

Maxwell's Equations
Maxwell's equations describe how an electric field can generate a magnetic field and vice-versa. These equations describe the relationship and behaviour of electric and magnetic fields.
Maxwell gave a set of 4 equations which are known as Maxwell's equations.
According to Maxwell's equations: - A flow of electric current will generate magnetic field and if the current varies with time magnetic field will also give rise to an electric filed.

Gauss's Law in electrostatics, $\oint E . d s = \frac{q}{ϵ _{o}}$
Gauss's Law in magnetism, $\oint B . d s = 0$
Faraday's Law of electromagnetic induction, $\oint E . d l = - \frac{d ϕ _{B}}{d t}$
Modified Amphere's circuital law, $\oint B . d l = μ_{o} (I_{C} + I_{D})$ where, $I_{C}$ is conduction current and $I_{D}$ is displacement current and given by $I_{D} = ϵ_{o} \frac{D ϕ _{E}}{d t}$ .

Maxwell was the first to determine the speed of propagation of EM waves is same as the speed of light. Experimentally it was found that:-

c = \frac{1}{μ _{o} ϵ _{o}}

. Maxwell's equations show that the electricity, magnetism and ray optics are all inter-related to each other.

Electromagnetic Waves

Electromagnetic waves are coupled time varying electric and magnetic fields that propagate in space.
Electric field is varying with time, and it will give rise to magnetic field, this magnetic field is varying with time and it gives rise to electric field and the process continues so on.
In the fig, red line represents the electric field and it varies in the form of a sine wave. The magnetic field as shown in the fig. represented by blue line.
The magnetic field will be a sine wave but in a perpendicular direction to the electric field. These both give rise to electromagnetic field.
If the electric field is along x-axis, magnetic field along y-axis, the wave will then propagate in the z-axis.
Electric and magnetic field are perpendicular to each other and to the direction of wave propagation.
Electric and magnetic fields which is time varying and coupled to each other they give rise to electromagnetic waves.

Sources of Electromagnetic Waves (EM):

EM waves are generated by electrically charged particle oscillates (accelerating charges). The electric field associated with the accelerating charge vibrates which generates the vibrating magnetic field. Both vibrating electric and magnetic fields give rise to EM waves.

Nature of EM waves:

EM waves are transverse waves.
The transverse waves are those in which the direction of disturbance or displacement in the medium is perpendicular to that of the propagation of the wave.
The particles of the medium are moving in a direction perpendicular to the direction of propagation of the wave.
Because of this EM waves are transverse waves in nature.
Electric field of EM wave is represented as: $E_{Y} = E_{0} ψ (k x - ω t)$ where $E_{y}$ = electric field along y-axis and x = direction of propagation of wave. Wave number $k = (2 π / λ)$
The magnetic field of EM wave is represented as: $B_{z} = B_{0} ψ (k x - ω t)$ where $B_{Z}$ = electric field along the z-axis and x = direction of propagation of the wave.

Energy of EM wave

Energy in EM waves is partly carried by an electric field and partly by the magnetic field.

Mathematically: -

Total energy stored per unit volume in EM wave, $E_{T} = Energy stored per unit volume by electric field + Energy stored per unit volume stored in magnetic field$ . i.e., $E_{T} = \frac{1}{2} E^{2} ϵ_{o} + \frac{1}{2} B^{2} / μ_{o}$
Experimentally it has been found that the; $Speed of the EM wave = Speed of the light$ $c = \frac{E}{B} \Rightarrow B = \frac{E}{c} ∴ E_{T} = \frac{1}{2} E^{2} ϵ_{o} + \frac{1}{2} \frac{E ^{2}}{c ^{2} μ _{o}}$ where $μ =$ permeability of the medium and $ϵ =$ permittivity of the medium.

Electromagnetic Spectrum

The systematic sequential distribution of electromagnetic waves in ascending or descending order of frequency or wavelength is known as the electromagnetic spectrum. The range varies from

1 0^{- 12} m

, to

1 0^{4}

m, i.e. from

γ

-rays to radio waves.

We see the uses of the electromagnetic waves in our daily life as:

Radio: A radio basically captures radio waves that are transmitted by radio stations. Radio waves can also be emitted by gases and stars in space. Radio waves are mainly used for TV/mobile communication.
Microwave: This type of radiation is found in microwaves and helps in cooking at home/office. It is also used by astronomers to determine and understand the structure of nearby galaxies and stars.
Infrared: It is used widely in night vision goggles. These devices can read and capture the infrared light emitted by our skin and objects with heat. In space, infrared light helps to map the interstellar dust.
X-ray: X-rays can be used in many instances. For example, a doctor can use an x-ray machine to take an image of our bones or teeth. Airport security personnel use it to see through and check bags. X-rays are also given out by hot gases in the universe.
Gamma-ray: It has a wide application in the medical field. Gamma-ray imaging is used to see inside our bodies. Interestingly, the universe is the biggest gamma-ray generator of all.
Ultraviolet: Sun is the main source of ultraviolet radiation. It causes skin tanning and burns. Hot materials that are in space also emit UV radiation.
Visible: Visible light can be detected by our eyes. Light bulbs, stars, etc. emit visible light.

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Electromagnetic Waves Revision Notes

Sources of Electromagnetic Waves (EM):

Nature of EM waves:

Energy of EM wave

Mathematically: -

Electromagnetic Spectrum

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Facebook SDK (Plugin)

Electromagnetic Waves Revision Notes

Sources of Electromagnetic Waves (EM):

Nature of EM waves:

Energy of EM wave

Mathematically: -

Electromagnetic Spectrum

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