Electromagnetic Waves: Explanation, Equations and Applications

Electromagnetic waves are a type of radiation that travels through space.

• They are produced when an electric field interacts with a magnetic field.
• The constitution of an oscillating magnetic field and electric fields gives rise to electromagnetic waves.
• Electricity and magnetism can be static, but they form waves when they change or move together.
• Magnetic and electric fields of an electromagnetic wave are perpendicular to each other and the direction of the wave.
• Electromagnetic waves are also considered to be the solutions to the fundamental equations of electrodynamics i.e. Maxwell’s Equations.  

Key Terms: Electric field, Electromagnetic Wave, Magnetic Field, Magnetic field lines, Electromagnetic Spectrum, Frequency, Wavelength, Speed of light, Intensity, Energy density

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What are Electromagnetic Waves? 

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According to Maxwell, a time-varying electric field gives rise to a time-varying magnetic field.

“The mutually perpendicular time-varying electric and magnetic fields give rise to electromagnetic waves that propagate with the speed of light at a right angle to both electric and magnetic fields.”

• The intensity and frequency of the time variation of the electric and magnetic fields define an electromagnetic wave.
• Examples of Electromagnetic Waves are Radio waves, Microwaves, Visible light, and X-rays.
• Electromagnetic waves are transverse waves that can travel through a vacuum like the speed of light i.e. 3 x 10⁸ m/s.

Electromagnetic Waves

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Graphical Representation of Electromagnetic Waves 

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Electromagnetic waves are represented by a sinusoidal graph.

• It consists of time-varying electric and magnetic fields that are perpendicular to each other and also to the direction of wave propagation.
• The nature of the electromagnetic waves is transverse.
• The highest point of the wave is called the crest, while the lowest point is called the trough.
• Electromagnetic waves move in free space or vacuum at a constant speed of 3 x 10⁸ m/s.
• Maxwell proposed the fundamental concept of electromagnetic radiation.
• Whereas Hertz empirically established the presence of an electromagnetic wave.

Graphical Representation of Electromagnetic Waves

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Mathematical Representation of Electromagnetic Waves

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A plane EM Wave traveling in the direction of the x-axis, having Electric field E and magnetic field B, is of the form 

E(x,t)= E_max cos(kx − ωt + Φ)

B(x,t)= B_max cos(kx − ωt + Φ)

Where

• E represents the electric field vector
• B represents the magnetic field vector
• E_max is the amplitude of the electric field
• B_max is the amplitude of the magnetic field
• k is the wave number

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Formation of Electromagnetic Waves 

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“An oscillating charge is a source of electromagnetic waves”.

• Oscillating charge has accelerated motion and if it oscillated with frequency f, then it produces EM waves of frequency f.
• Neither a charge at rest nor a charge in steady motion can be the source of electromagnetic waves.
• If a charge moves with uniform velocity, it will produce an electric and magnetic field of a stationary nature.
• But if the charge accelerates, then it will produce an electric and magnetic field that varies with time and produces an electromagnetic wave.
• These waves transfer energy through space.
• These waves, in a vacuum, travel at a constant velocity of 3 x 10⁸ ms^-1.
• The movement of an electromagnetic wave through any medium or vacuum can be described through the Electromagnetic waves equation.

Formation of Electromagnetic Waves

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Transverse Nature of Electromagnetic Waves

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A transverse wave is a moving wave whose oscillations are perpendicular to the path of the propagation.

• A changing electric field produces a changing magnetic field and vice-versa.
• It gives rise to a transverse wave known as an electromagnetic wave.
• The variations of the electric field and magnetic field are mutually perpendicular to each other and to the direction of propagation of the wave.
• Therefore the electromagnetic waves are transverse in nature.

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Electromagnetic Wave Equation

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The electromagnetic wave equation defines how electromagnetic waves propagate in a vacuum or through a medium.

• The electromagnetic wave equation is a partial differential equation of second order.
• It is a 3D representation of the wave equation.

The homogeneous form of the equation can be written as

\((v^2_{ph}\nabla ^2-\frac{\delta ^2}{\delta t^2})E=0\)

\((v^2_{ph}\nabla ^2-\frac{\delta ^2}{\delta t^2})B=0\)

Where \(v_{ph}= \frac{1}{\sqrt{\mu \epsilon}}\)

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Speed of Electromagnetic Wave 

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The speed of electromagnetic waves is given by the formula

\(c= \frac{1}{\sqrt{\mu_o \epsilon_o}}\)

Where

• c = speed of light 
• μ₀ is the absolute permeability of the free space
• ε₀ is the absolute permittivity of the free space

In a material medium, the speed of the electromagnetic waves is given by

\(c= \frac{1}{\sqrt{\mu \epsilon}}\)

Where

• μ is the permeability of the medium
• ε is the permittivity of the medium

The speed of electromagnetic waves can also be given by

\(c=\frac{E_o}{B_o}\)

Where

• E_o is the amplitude of the electric field
• B_o is the amplitude of the magnetic field

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Energy Density of Electromagnetic Waves

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The energy density of an electromagnetic wave is defined as the energy per unit volume of the space in which it travels.

Electromagnetic waves carry energy and this energy is shared equally by the electric and magnetic field

In electromagnetic waves, both electric and magnetic fields vary sinusoidally in space and time. Therefore the average energy density of the electromagnetic wave can be obtained by

\(U_{av}=\frac {1}{2}\epsilon_o E^2_{rms}+\frac {1}{2}\frac {B^2_{rms}}{\mu_o}\)

Where

• U_av is the average energy density of electromagnetic wave
• E_rms is the rms value of the electric field
• B_rms is the rms value of the magnetic field

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Intensity of Electromagnetic Waves

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The intensity of an electromagnetic wave is defined as the energy crossing per unit area per unit time perpendicular to the direction of the propagation of the wave.

Mathematically, it is given by

\(I = \epsilon_ocE^2_rms=\frac {1}{2}\epsilon_ocE^2_o\)

Where

• ε_o is the absolute permittivity of the free space
• E_rms is the rms value of the electric field
• c is the speed of the wave
• E_o is the amplitude of the electric field.

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Electromagnetic Spectrum

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The whole range of frequency/wavelength of the electromagnetic waves arranged in ascending or descending order is known as electromagnetic spectrum.

The wavelength ranges of visible light are from approx. 400 nm to approx. 700 nm.

The wavelength for the various spectra of light is as follows

• Radio Waves: greater than 0.1 m
• Microwave: 0.1m to 1 mm
• Infra-red waves: 1 mm to 700 nm
• Visible light: 700 nm to 400 nm
• Ultraviolet: 400 nm to 1nm
• X-rays:1nm to 10^-3 nm
• Gamma rays: less than 10^-3 nm

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Applications of EM Waves

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The following are the applications of the electromagnetic waves

• Infrared radiation is used in security cameras and is also used for night vision.
• Forged banknotes can also be detected with the help of UV rays. Under UV light, real notes won’t turn fluorescent.
• RADARS also makes use of Electromagnetic waves.
• EM waves also play a crucial role in communication technology.

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Things to Remember

• The waves that are produced when an electric field comes into contact with a magnetic field are known as Electromagnetic Waves or EM waves.
• These waves are also considered to be the solutions of the fundamental equations of electrodynamics i.e. Maxwell’s equation. 
• EM Waves are transverse in nature.
• They are represented by these sinusoidal graphs which consist of time-varying magnetic and electric fields.
• The charges that are accelerated, for example, the oscillating charge, radiate these EM waves. 
• An electric field generally is produced through a particle that is charged.
• This produced electric field then exerts a force on other similar charged particles.
• Infrared radiation is used in security cameras and is also used for night vision.
• EM waves also play a crucial role in communication technology.

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Previous Year Questions

1. A parallel plate capacitor of capacitance 20μF is being charged by… [NEET 2019]
2. A radiation of energy 'E ' falls normally on a perfectly reflecting surface… [NEET 2015]
3. An electromagnetic wave of frequency υ = 3.0 MHz passes from… [NEET 2013]
4. Biological importance of ozone layer is… [NEET 2001]
5. If ε₀ and μ₀ are the electric permittivity and magnetic permeability… [NEET 1997]
6. Light with an energy flux of 25×10⁴Wm⁻² falls on a perfectly reflecting… [NEET 2014]
7. The condition under which a microwave oven heats up… [NEET 2013]
8. The electric field associated with an e.m. wave in vacuum is... [NEET 2012]
9. The ratio of contributions made by the electric field… [NEET 2020]
10. The velocity of electromagnetic wave is parallel to… [NEET 2002]
11. Wavelength of light of frequency 100 Hz… [NEET 1999]
12. What is the cause of ''Green house effect''… [NEET 2002]
13. Which of the following statement is false for the properties of… [NEET 2010]
14. If →E and →B are the electric and magnetic field vectors of… [BITSAT 2019]
15. Which of the following rays is emitted by a human body… [VITEEE 2010]
16. A 100Ω resistance and a capacitor of 100Ω reactance are connected in… [NEET 2016]
17. The electric field part of an electromagnetic wave in a medium is… [NEET 2009]
18. The electric and magnetic field of an electromagnetic wave are… [NEET 1994]
19. In which of the following, emission of electrons does not take place… [NEET 1990]
20. If λv,λx,λm represent the wavelengths of visible light… [NEET 2005]