Electromagnetic Waves, Definition, Maxwell’s Equations, Spectrum and Uses

Electromagnetic Waves in NEET Physics syllabus is a crucial one and carries a weightage of about 3% in the exam. Electromagnetic waves are created when electric and magnetic fields change together in space and time. They can travel without any medium of travel as do sound waves. The students can study the nature of light and how it travels through space. 

The behaviour of light, radio signals, and X-rays can be analyzed and understood with the help of the concept of Electromagnetic waves. Electromagnetic waves are based on the research work of James Clerk Maxwell. Maxwell combined the two previously independent fields, electricity and magnetism, through a set of differential equations called Maxwell’s equations. The equations showed that electromagnetic waves consist of oscillating electric and magnetic fields that are perpendicular to each other and travel through space at the speed of light.

The various communication systems, including mobile phones, radio, microwaves, medical X-rays, TV signals, satellite signals, etc., are all based on the behaviour of electromagnetic waves. The nature and sources of electromagnetic waves, mathematical derivation of the electromagnetic waves are some important concepts that need to be studied in detail for NEET Physics preparation.

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What are Electromagnetic Waves?

EM waves are defined as the waves which are generated due to the vibrations of electric and magnetic fields perpendicular to each other. In other words, an EM wave has an oscillating magnetic field and an electric field which is perpendicular to the direction of wave motion. The EM waves are called as electromagnetic waves.

These waves do not require a medium to travel through it, hence they can travel even in vacuum. Speed of EM wave is equal to the speed of light i.e. 3 × 108 m/s. The EM wave transports energy and momentum. Momentum can produce pressure when it strikes a surface.

EM waves are transverse in nature. In other words, both the fields oscillate perpendicular to the direction of wave propagation. Light, radio waves, microwaves, infrared, ultraviolet, X-rays, gamma rays are some of the examples of electromagnetic waves.

Also Read: Electromagnetic Waves NEET Notes

Modified Ampere’s Law

In order to get electromagnetic waves, we have to first fix Ampere’s law. Ampere’s circuital law states that the line integral of the magnetic field around a closed loop is equal to μ₀ times the current passing through it. It is given by: 

∮ B · dl = μ₀ I 

Maxwell realised that there was something amiss in the original equation when the electric fields were changing. For example, there is no conduction current between the plates of a capacitor when it is charging. This would imply that no magnetic field is produced which is not true. The above problem was corrected by adding a new term called the displacement current. This completes Ampere’s law. 

The modified Ampere’s law derivation includes both conduction current and displacement current. The new equation becomes:

∮ B · dl = μ₀ (I + I_d) 

where I_d = ε₀ (dΦ_E/dt) is the displacement current that results due to changing electric fields. This fix made the law obey the principle of continuity of current.

Also Read: Electromagnetic Waves MCQs

Displacement Current

The displacement current in a capacitor is another of Maxwell’s fundamental discoveries. When a capacitor is being charged, charge accumulates on one of the plates and the other plate, so that there is a changing electric field in the space between the plates. Although there is no real current between the plates, there is a time-varying electric field which gives rise to a magnetic field.

This time varying electric field acts as a current and this is called the displacement current. The displacement current is given by the equation:

I_d = ε₀ (dΦ_E/dt) 

Where, 

ε₀ = Permittivity of free space, 

Φ_E = Electric flux. 

We see that a displacement current has the same effect as a real current. That is, it gives rise to magnetic fields and is also required for the creation of electromagnetic waves. If there were no displacement current, the continuity of current in a circuit containing a capacitor would be inexplicable.

Maxwell’s Equations

James Clerk Maxwell arranged the four laws of electricity and magnetism together, now known as Maxwell’s equations (in electromagnetic theory). They explain how electric and magnetic fields interact with each other and how electromagnetic waves are created and propagate. These are as follows: 

Gauss’s law for electricity

The electric flux passing through any closed surface is equal to the total charge enclosed within it divided by the permittivity of free space, ε₀.

∮ E · dA = Q/ε₀ 

Gauss’s law for magnetism 

Magnetic monopoles do not exist and therefore the net magnetic flux through any closed surface is zero.

∮ B · dA = 0 

Faraday’s law of electromagnetic induction

A time-varying magnetic field creates an electric field.

∮ E · dl = -dΦ_B/dt 

Ampere-Maxwell law, or, the modified Ampere’s law

A time-varying electric field creates a magnetic field.

∮ B · dl = μ₀ (I + ε₀ dΦ_E/dt) 

These four equations collectively describe how electric and magnetic fields are created and how electromagnetic waves propagate. The two fields sustain each other by creating a time-varying field, which causes the other to generate. As a result of this interaction, an electromagnetic wave propagates in space.

Also Read: Electromagnetic Waves Important Questions

Sources of Electromagnetic Waves

Whenever an electric charge accelerates, it produces electromagnetic waves. If an electrically charged particle speeds up, slows down or changes its direction, it emits electromagnetic radiation. Typical examples of sources of electromagnetic waves include:

• Antennas (oscillating electric charges), for example, radio and TV signals.

• Atoms (oscillating or vibrating electrons), for example, light emission.

• Stars, and the Sun (oscillating or accelerated particles), for example, cosmic and solar radiation.

• X-ray tubes (accelerated electrons), for example, X-rays.

In the laboratory, oscillating electric circuits or lasers are also used to produce electromagnetic waves. In all these cases, the continuous change of the electric and magnetic fields produces self-propagating electromagnetic waves.

Equation of Electromagnetic Waves

The equation for electromagnetic waves signifies the coupling between the electric field and magnetic field in free space. The wave equations for the electric field and magnetic field can be derived from Maxwell’s equations as:

∇²E = μ₀ε₀ (∂²E/∂t²) 

∇²B = μ₀ε₀ (∂²B/∂t²) 

The solutions to these equations are given as plane electromagnetic waves travelling with a velocity v = 1/√(μ₀ε₀) = 3 × 108 m/s (the speed of light).

The wave equations suggest that the electric field and the magnetic field vary sinusoidally and in phase with each other. The direction of propagation is given by the cross product of the directions of the electric field and magnetic field.

Important Characteristics and Nature of Electromagnetic Waves

They are transverse waves and the electric and magnetic fields are perpendicular to each other and to the direction of propagation.

• Speed of propagation is the speed of light (3 × 108 m/s) in free space.

• Can propagate in free space as well as in material media.

• Energy carried by electric and magnetic fields is equal.

• The direction of propagation is given by their vector product E and B fields.

• Reflection, refraction, diffraction and interference are similar to those of light waves.

• Speed and wavelength vary with the refractive index of the medium.

• Because of these properties, electromagnetic waves are the fundamental concepts in optics, communication and medical image processing systems.

The Poynting Vector

The vector that represents the time rate of energy transfer or power per unit area is the Poynting vector. It is the vector product of the electric field and magnetic field divided by μ₀:

S = (E × B) / μ₀ 

The Poynting vector points in the direction of energy flow, and its magnitude is equal to power intensity. It can be used to calculate the energy that passes through a given area per second, in the direction of propagation.

This way, the Poynting vector bridges the gap between the electric and magnetic aspects of electromagnetic waves, and the energy they carry.

Intensity of Electromagnetic Wave

Intensity of electromagnetic wave, as the name suggests is the average power transported per unit area. It is associated with the Poynting vector and is given by the time average of the Poynting vector magnitude.

I = ⟨S⟩ = 1⁄2 ε₀ c E₀² 

Where, 

E₀ = Maximum electric field amplitude, 

c = Speed of light. 

From the above equation, we can conclude that intensity is directly proportional to the square of the amplitude of the electric field. Greater the field strength, greater is the intensity. The intensity of light determines how bright it appears or how strong a signal is.

Radiation Pressure on Surface 

Electromagnetic waves transfer energy and momentum to a surface. When the radiation is incident on a surface, it exerts a radiation pressure. The radiation pressure can be calculated from the intensity of the wave and the type of surface on which the radiation falls

P = I/c for a perfectly absorbing surface 

P = 2I/c for a perfectly reflecting surface 

Here, I = intensity of wave and c = speed of light in vacuum.

The pressure is very small but it is of considerable importance in astrophysics and space technology. The radiation pressure of sunlight on satellite panels changes their velocity slightly.

Refractive Index of Medium 

The refractive index of medium is the factor by which the speed of an electromagnetic wave is reduced in a medium as compared to vacuum. It is given by 

n = c/v 

Where, 

c = speed of light in vacuum, 

v = speed of light in medium 

The higher the refractive index, the more optically dense the medium and slower is the speed of light. This phenomenon is utilized in optics, lenses, and fiber communication systems.

Electromagnetic Waves Spectrum

The electromagnetic spectrum is a range of all electromagnetic waves arranged according to their frequency or wavelength. It covers waves from the lowest frequency radio waves to the highest frequency gamma rays.

Uses of Electromagnetic Waves

The various applications of Electromagnetic waves in different fields are as follows:

• Radio waves: Used in radio, television, and mobile phones 

• Microwaves: Used in Microwave ovens, Radar systems and satellite communication

• Infrared waves: Used in remote controls, Thermal cameras and Night vision cameras

• Visible light: It helps in vision, Lighting and photography 

• UV rays: Used for sterilization and detecting fake currency 

• X rays: Used for medical imaging and Security scanning 

• Gamma rays: Used in cancer treatment and studying atomic structures

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Electromagnetic Waves PDF

Candidates can now download this Electromagnetic Waves PDF to revise this complete topic once for NEET Physics preparation. The file consists of all important concepts of electromagnetic waves, including modified Ampere’s law derivation, displacement current in capacitor, Maxwell’s equations, sources of electromagnetic waves, and the electromagnetic spectrum and its uses.

The Electromagnetic Waves PDF can help candidates develop conceptual clarity and solid preparation for NEET. Electromagnetic Waves have about 3% weightage in the NEET exam, and candidates can download the file to revise this chapter at any time and understand the equation of electromagnetic waves, Poynting vector, intensity, and radiation pressure in a clear and well-organized way.

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