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Electromagnetic Waves:

An electromagnetic wave is a wave that propagates when electric and magnetic fields fluctuate together.

Plane progressive electromagnetic wave equation:

E = E0 sin ω (t – x/c)

B = B0 sin ω (t – x/c)

Here, ω = 2πf

Properties of elctromagnetic wave:

  • Since these waves are transverse in nature, a medium is not necessary for their propagation.

  • These waves move through space at the speed of light, or 3 times 108 metres per second.

  • It propagates while carrying energy. The energy associated with the wave increases with frequency.

  • It has the ability to impart its energy onto the object it impacts.

  • Its spread complies with the inverse square law (e).

  • Information can be carried using it.

  • It may reflect or refractive alter.

  • Diffraction patterns can be created by splitting and recombining it.

  • It can travel a long way. As far away as the next planet, the radiation produced by a straightforward 100 volt, 1 MHz sine wave fed into an appropriate antenna can be heard.

  • It moves straight lines only.

  • By reflecting off of the ionosphere, it can be bent around the circumference of the Earth.

  • It is able to go through walls.

  • By blocking its path with a metal rod, a loop, a parabolic metal dish, or a horn, it can be captured and launched into the atmosphere.

  • The fields of E and B are parallel to one another.

  • The fields of E and B are in phase (both reach a maximum and minimum at the same time).

  • The E and B fields are parallel to the arrow of motion (transverse waves).

Speed of electromagnetic wave:

c = 1/√µ0ε0

Here, µ0 is permeability of free space and ε0 is the permitivity `of free space.

c = E0/B0

Here E0 and B0 are maximum values of electric and magnetic field vector.

Total radiant flux (Power):

P = q2a2/6πε0c2

Poynting vector:

The vector S, also known as the poynting vector, describes the rate of energy flow in an electromagnetic wave.

S = (1/µ0) [EB]

SI unit of S is watt/m2

Electric field and magnetic field vectors each contain an equal amount of electromagnetic wave energy.

Average electric energy density

UE = ½ ε0E2 = ¼ ε0E02 S

Average magnetic energy density

UB = ½ (B2/µ0) = ¼ (B02/µ0)

Intensity of electromagnetic Wave:

It is defined as an energy crossing per unit area per unit time that is perpendicular to the electromagnetic wave's directions of propagation.

I = <µ> c = ½ (ε0E02c)

Displacement current:

It is a current that develops in an area where the electric field and subsequently the electric flux are subject to temporal variation.

Current displacement, ID = 0 (dE/dt)

E is the electric flux in this case.

Ampere- Maxwell law:

B.dl = µ0 (I + ID)

Where, µ0 = Permeability = 4π10-7 V/Am

Maxwell’s Equations

(a) E.dS = q/ε0

This equation is Gauss’s law in electrostatics.

(b) E.dS = 0

This equation is Gauss’s law in magnetostatics.

(c) E.dl = (– d/dt) ?B.dS

This equation is Faraday’s law of electromagnetic Induction.

(d) B.dl = µ0 [I +ε0 (dφE/dt)]

This equation is Ampere – Maxwell law.

Electromagnetic spectrum (consists of EM waves of all frequencies)

(a) radio waves (biggest wavelength, smallest frequency)

(b) microwaves

(c) infrared waves

(d) visible light (ROY G BIV)

(e) ultraviolet light

(f) x-rays

(g) gamma rays (smallest wavelength, highest frequency)

Speed of waves:

  • v = fλ

  • EM waves move slower through materials than they do in a vacuum.

  • n = c/v, where v is the material's index of refraction for light,

  • The wavelength changes but the frequency does not when a wave travels through different materials:

  • λ = λ0/n, where λ0 is the wavelength in vacuum


(a) For an electromagnetic wave, the electric field's direction is assumed to be the direction of polarisation.

(b) A polarising filter reduces the intensity of transmitted light when an EM wave passes through it:

I = ½ I0 initially unpolarized light

I = I0 cos2θ initially polarized light

After light passes through a filter, it is polarized in the direction of the filter.

Right Hand Rule:

E and B are perpendicular to one another and in phase in an electromagnetic wave travelling in the positive x direction. After pointing the fingers in the direction of E and curling them toward B, the right hand's thumb indicates the direction of propagation (palm towards B).

Spectrum Propagation in Electrons:

In radio wave communication between two locations, the transmitter antenna at one location emits electromagnetic waves that travel through space and arrive at the receiving antenna at the other location.

Electromagnetic Spectrum:

The term "electromagnetic spectrum" refers to the arrangement of electromagnetic radiations in order of their wavelength or frequency.

Radio and microwaves: used in radio and television communication

Infrared rays are used to:

In order to:

(a) relieve muscular tension

(b) take pictures in smoke or fog

(c) keep plants warm in greenhouses

(d) use infrared photography for weather forecasting

The use of ultraviolet rays

(A) When researching molecular structure

(b) When sanitising surgical equipment.

(c) Fingerprints are used to identify forged documents.

X-rays are used

(a) spotting errors, cracks, flaws, and holes in metal products.

(b) When researching crystal structure.

(c) In order to find pearls in oysters.

γ-rays are used for the study of nuclear structure.

Some previous years sample questions on Electromagnetic Waves.

1. Question Arrange the following electromagnetic radiations per quantum in the order of increasing energy: [JEE (Main) 2016] A : Blue light B : Yellow light C : X-ray D : Radiowave

2. Question Out of the following options which one can be used to produce a propagating electromagnetic wave? [NEET 2016]

  • (A) A chargeless particle

  • (B) An accelerating charge

  • (C) A charge moving at constant velocity

  • (D) A stationary charge

3. Question

A red LED emits light at 0.1 watt uniformly around it. The amplitude of the electric field of the light at a distance of 1 m from the diode is [JEE Main 2015]

  • (A) 1.73 V/m

  • (B) 2.45 V/m

  • (C) 5.48 V/m

  • (D) 7.75 V/m

4. Question The electric field of an electromagnetic wave in free space is given by

where t and x are in seconds and metres respectively. It can be inferred that (a) The wavelength λ is 188.4 m (b) The wave number k is 0.33 rad/m (c) The wave amplitude is 10 V/m (d) The wave is propagating along +x direction

Which one of the following pairs of statements is correct? [CBSE AIPMT 2010]

  • (A) (c) & (d)

  • (B) (a) and (b)

  • (C) (b) & (c)

  • (D) (a) & (c)

5. Question The electric and magnetic field of an electromagnetic wave are [CBSE AIPMT 2007]

  • (A) in opposite phase and perpendicular to each other

  • (B) in opposite phase and parallel to each other

  • (C) in phase and perpendicular to each other

  • (D) in phase and parallel to each other.

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