DISPLACEMENT CURRENT
(i) Circuit with Capacitor
Let us consider a circuit containing the capacitor as shown in fig. 21.1
Circuit Diagram: A capacitor connected in a circuit with current flowing through connecting wires but not through the space between plates
(ii) Ampere's Circuital Law
According to Ampere's circuital law, the line integral of magnetic field along any closed path is μ₀ times the total current enclosed by the closed path. Mathematically:
In this law it is assumed that conduction current flows through the connecting wires charging the condenser plates but no current flows in the space in between the plates. Actually it is not true.
Illustration 1: In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency 2 × 10¹⁰ Hz and amplitude 48 V/m. The amplitude of oscillating magnetic field will be:
Options:
(A) 1.6 × 10⁻⁸ Wb/m²
(B) 16 × 10⁻⁸ Wb/m²
(C) 12 × 10⁻⁷ Wb/m²
(D) 1.2 × 10⁻⁷ Wb/m²
Solution:
(B) Oscillating magnetic field
B = E/c = 48/(3 × 10⁸) = 16 × 10⁻⁸ Wb/m²
(iii) Maxwell's Modification
When the circuit is closed, conduction current flows from the plate P of the capacitor to the other plate Q through the conducting wires. Maxwell suggested that due to time varying electric field between the plates, an electric current, called displacement current (I_D), also flows across the space between the plates of the capacitor.
(iv) Continuous Current Flow
Thus, there is a continuous flow of current in a capacitive circuit also, through the conducting wire there is flow of conduction current I_C and through the space across the plates of capacitor, there is flow of displacement current I_D.
(v) Ampere-Maxwell's Circuital Law
Maxwell pointed out that in Ampere's circuital law, the current I should be treated as total current i.e., the sum of the conduction current I_C and displacement current I_D and modified the law as:
∮ B⃗ · dl⃗ = μ₀(I_C + I_D)
It is called the Ampere-Maxwell's circuital law.
(vi) Displacement Current Definition
The displacement current is defined as:
I_D = ε₀ (dΦ_E/dt)
where Φ_E is the electric flux linked between the plates of the capacitor at any instant.
Therefore Ampere-Maxwell circuital law may be expressed as:
∮ B⃗ · dl⃗ = μ₀[I_C + ε₀(dΦ_E/dt)]
Illustration 2: A parallel plate capacitor of plate separation 2 mm is connected in an electric circuit having source voltage 400V. If the plate area is 60 cm², then the value of displacement current for 10⁻⁶ sec. will be:
Options:
(A) 1.062A
(B) 1.062 × 10⁻²A
(C) 1.062 × 10⁻³A
(D) 1.062 × 10⁻⁴A
Solution:
(D) I_D = ε₀(dΦ_E/dt) = ε₀(d(EA)/dt) = ε₀A(dE/dt) = ε₀A(V/d)/t
I_D = (8.85 × 10⁻¹² × 400 × 60 × 10⁻⁴)/(2 × 10⁻³ × 10⁻⁶) = 1.062 × 10-4A
Illustration 3: In an electric circuit, there is a capacitor of reactance 100Ω connected across the source of 220V. The displacement current will be:
Options:
(A) 2.2A
(B) 0.22A
(C) 4.2A
(D) 2.4A
Solution:
(A) Displacement current and conduction current are equal.
ID = E/Z = 220/100 = 2.2A
(vii) & (viii) Important Properties
- The conduction current and the displacement current are always equal, i.e., IC = ID
- Like conduction current, the displacement current is also the source of magnetic field
Also Read: Electrostatic Potential and Capacitance
MAXWELL'S EQUATIONS AND LORENTZ FORCE
The existence of electro-magnetic waves that propagate through the space in the form of varying electric and magnetic fields has been predicted by the four basic laws of electromagnetism which are called Maxwell's equations.
(i) Maxwell's First Equation - Gauss's Law in Electrostatics
It states that the total electric flux through any closed surface is equal to 1/ε₀ times the net charge enclosed by
Mathematically,
∮ E⃗ · ds⃗ = q/ε₀
This equation is called Maxwell's first equation.
(ii) Maxwell's Second Equation - Gauss's Law in Magnetism
It states that the net magnetic flux crossing any closed surface is always zero.
Mathematically,
∮ B⃗ · ds⃗ = 0
This equation is called Maxwell's second equation. A direct consequence of this equation is that the magnetic monopoles do not exist.
(iii) Maxwell's Third Equation - Faraday's Law of Electromagnetic Induction
It states that the induced emf produced in a circuit is numerically equal to the rate of change of magnetic flux through it.
Mathematically,
ε = -dΦ_B/dt
But ε = ∮ E⃗ · dl⃗ = Line integral of electric field.
∮ E⃗ · dl⃗ = -dΦ_B/dt
This equation is called Maxwell's third equation.
The negative sign in this equation indicates that the induced emf produced opposes the rate of change of magnetic flux.
Illustration 4: A point source of electromagnetic radiation has an average power output of 800W. The maximum value of electric field at a distance 3.5m from the source will be:
Options:
(A) 56.7 V/m
(B) 62.6 V/m
(C) 39.3 V/m
(D) 47.5 V/m
Solution:
(B) Intensity of electromagnetic wave given is by
Illustration 5: In the above problem, the maximum value of magnetic field will be:
Options:
(A) 2.09 × 10⁻⁵ T
(B) 2.09 × 10⁻⁶ T
(C) 2.09 × 10⁻⁷ T
(D) 2.09 × 10⁻⁷ T
Solution:
(C) The maximum value of magnetic field is given by
B_m = E_m/c = 62.6/(3 × 10⁸) = 2.09 × 10⁻⁷ T
(iv) Maxwell's Fourth Equation - Maxwell-Ampere Circuital Law
It states that the line integral of magnetic field along a closed path is equal to μ₀ times the total current (i.e., sum of conduction and displacement currents threading the surface bounded by that closed path)
Mathematically,
∮ B⃗ · dl⃗ = μ₀[I_C + ε₀(dΦ_E/dt)]
This equation is called Maxwell's fourth equation.
(v) Lorentz Force
The vector sum of electric force and magnetic force on any charged particle is called the Lorentz force.
F⃗ = q[E⃗ + (v⃗ × B⃗)]
The above five equations give a complete description of all electromagnetic interactions.
Do Check - Current Electricity
PRODUCTION OF ELECTROMAGNETIC WAVES
(i) Maxwell's Theory
According to Maxwell, an accelerated charge sets up a magnetic field in its neighbourhood. The magnetic field, in turn, produces an electric field in that region. Both these fields vary with time and act as sources for each other.
(ii) Oscillating Charge
As oscillating charge is accelerated continuously, it will radiate electromagnetic waves continuously.
(iii) Hertz's Demonstration (1888)
In 1888, Hertz demonstrated the production of electromagnetic apparatus is shown schematically in fig.
Hertz's Apparatus:
Input → Transmitter (+/-) → Receiver
Induction coil connected to spherical electrodes
(iv) Transmitter Operation
An induction coil is connected to two spherical electrodes with a narrow gap between them. It acts as a transmitter. The coil provides short voltage surges to the spheres making one positive and the other negative. A spark is generated between the spheres when the voltage between them reaches the breakdown voltage for air. As the air in the gap is ionised, it conducts more rapidly and the discharge between the spheres becomes oscillatory.
(v) LC Circuit Equivalent
The above experiment arrangement is equivalent to an LC circuit, where the inductance is that of the loop and the capacitance is due to the spherical electrodes.
(vi) Wave Radiation
Electromagnetic waves are radiated at very high frequency (100 MHz) as a result of oscillation of free charges in the loop.
(vii) & (viii) Detection
- Hertz was able to detect these waves using a single loop of wire with its own spark gap (the receiver)
- Sparks were induced across the gap of the receiving electrodes when the frequency of the receiver was adjusted to match that of the transmitter
HISTORY OF ELECTROMAGNETIC WAVES
(i) 1865 - Maxwell's Prediction
In year 1865, Maxwell predicted the electromagnetic waves theoretically. According to him, an accelerated charge sets up a magnetic field in its neighborhood.
(ii) 1887 - Hertz's Production
In 1887, Hertz produced and detected electromagnetic waves experimentally at wavelength of about 6m.
(iii) J.C. Bose's Contribution
Seven year later, J.C. Bose became successful in producing electromagnetic waves of wavelength in the range 5 mm to 25 mm.
(iv) 1896 - Marconi's Discovery
In 1896, Marconi discovered that if one of the spark gap terminals is connected to an antenna and the other terminal is earthed, the electromagnetic waves radiated could go upto several kilometers.
(v) Antenna System
The antenna and the earth wires form the two plates of a capacitor which radiates radio frequency waves. These waves could be received at a large distance by making use of an antenna earth system as detector.
(vi) 1899 - First Wireless Communication
Using these arrangements; in 1899 Marconi first established wireless communication across the English channel i.e. across a distance of about 50 km.
PROPERTIES OF ELECTROMAGNETIC WAVES
(i) Wave Equations
The electric and magnetic fields satisfy the following wave equations, which can be obtained from Maxwell's third and fourth equations.
(ii) Speed of Light
Electromagnetic waves travel through vacuum with the speed of light c, where
c = 1/√(μ₀ε₀) = 3 × 10⁸ m/s
(iii) Transverse Nature
The electric and magnetic fields of an electromagnetic wave are perpendicular to each other and also perpendicular to the direction of wave propagation. Hence, these are transverse waves.
(iv) Relationship between E and B
The instantaneous magnitude of E⃗ and B⃗ in an electromagnetic wave are related by the expression
E/B = c
(v) Energy Flow - Poynting Vector
Electromagnetic waves carry energy. The rate of flow of energy crossing a unit area is described by the Poynting vector S⃗
where
S⃗ = (1/μ₀)(E⃗ × B⃗)
(vi) Radiation Pressure
Electromagnetic waves carry momentum and hence can exert pressure (P) on surfaces, which is called radiation pressure. For a perfectly absorbing surface
P = S/c
and if incident on a perfectly reflecting surface
P = 2S/c
(vii) Sinusoidal Wave Representation
The electric and magnetic fields of a sinusoidal plane electromagnetic wave propagating in the positive x-direction can also be written as
E⃗ = E_m sin(kx - ωt)
B⃗ = B_m sin(kx - ωt)
where ω is the angular frequency of the wave and k is wave number which are given by
ω = 2πf and k = 2π/λ
(viii) Intensity
The intensity of a sinusoidal plane electromagnetic wave is defined as the average value of Poynting vector taken over one cycle.
(ix) Fundamental Sources
The fundamental sources of electromagnetic waves are accelerating electric charges. For example radio waves emitted by an antenna arise from the continuous oscillations (and hence acceleration) of charges within the antenna structure.
(x) Superposition Principle
Electromagnetic waves obey the principle of superposition.
(xi) Light Vector
The electric vector of an electromagnetic field is responsible for all optical effects. For this reason electric vector is called a light vector.
Illustration 6: DIn an electromagnetic wave, the amplitude of electric field is 1V/m. The frequency of wave is 5 × 10¹⁴ Hz. The wave is propagating along z-axis. The average energy density of electric field, in Joule/m³, will be:
Options:
(A) 1.1 × 10⁻¹¹
(B) 2.2 × 10⁻¹²
(C) 3.3 × 10⁻¹³
(D) 4.4 × 10⁻¹⁴
Solution:
(B) Average energy density is given by
Illustration 7: To establish an instantaneous displacement current of 2A in the space between two parallel plates of 1μF capacitor, the potential difference across the capacitor plates will have to be changed at the rate of:
Options:
(A) 4 × 10⁴ V/s
(B) 4 × 10⁶ V/s
(C) 2 × 10⁴ V/s
(D) 2 × 10⁶ V/s
Solution: (D)
ELECTROMAGNETIC SPECTRUM
(i) Definition
The orderly distribution of electromagnetic waves (on the basis of wavelength or frequency) in the form of distinct groups having widely differing properties is called the electromagnetic spectrum.
The following table gives a complete and detailed picture of electromagnetic spectrum
(ii) Various parts of electromagnetic spectrum
| S. No. | Radiation | Discoverer | How produced | Wavelength range | Frequency range | Energy range | Properties | Application |
| 1. | γ-Rays | Henry Becquerel and Madam Curie | Due to decay of radioactive nuclei | 10⁻¹⁴ m to 10⁻¹⁰ m | 3 × 10²² Hz to 3 × 10¹⁸ Hz | 10⁷eV – 10⁴ eV | (a) High penetrating power (b) Uncharged (c) Low ionising power |
(a) Gives information on nuclear structure (b) Medical treatment etc. |
| 2. | X-Rays | Roentgen | Due to collisions of high energy electrons with heavy targets | 6 × 10⁻¹⁰ m to 10⁻⁹ m | 5 × 10¹⁹ Hz to 3 × 10¹⁷ Hz | 2.4 × 10⁵ eV to 1.2 × 10³ eV | (a) Low penetrating power (b) Other properties similar to γ-rays except wavelength |
(a) Medical diagnosis and treatment (b) Study of crystal structure (c) Industrial radiography |
| 3. | Ultraviolet Rays | Ritter | By ionised gases, sun lamp spark etc. | 6 × 10⁻¹⁰ m to 3.8 × 10⁻⁷ m | 3 × 10¹⁷ Hz to 5 × 10¹⁹ Hz | 2×10³ eV to 3eV | (a) All properties similar to visible light (b) Photo-electric effect |
(a) To detect adulteration (b) Sterilization of water due to its destructive action on bacteria |
| 4. | Visible Light | Newton | Outer orbit electron transitions in atoms, gas discharge tube, incandescent | 3.8 × 10⁻⁷ m to 7.8 × 10⁻⁷ m | 8 × 10¹⁴ Hz to 4 × 10¹⁴ Hz | 3.2 eV to 1.6eV | (a) Sensitive to human eye | (a) To see objects (b) To study molecular structure |
| - | (a) Violet | - | - | 3.9×10⁻⁷ m to 4.55×10⁻⁷ m | 7.69×10¹⁴ Hz to 6.59×10¹⁴ Hz | - | - | - |
| - | (b) Blue | - | - | 4.55×10⁻⁷ m to 4.92×10⁻⁷ m | 6.59×10¹⁴ Hz to 6.10×10¹⁴ Hz | - | - | - |
| - | (c) Green | - | - | 4.92×10⁻⁷ m to 5.77×10⁻⁷ m | 6.10×10¹⁴ Hz to 5.20×10¹⁴ Hz | - | - | - |
| - | (d) Yellow | - | - | 5.77×10⁻⁷ m to 5.97×10⁻⁷ m | 5.20×10¹⁴ Hz to 5.03×10¹⁴ Hz | - | - | - |
| - | (e) Orange | - | - | 5.97×10⁻⁷ m to 6.22×10⁻⁷ m | 5.03×10¹⁴ Hz to 4.82×10¹⁴ Hz | - | - | - |
| - | (f) Red | - | - | 6.22×10⁻⁷ m to 7.80×10⁻⁷ m | 4.82×10¹⁴ Hz to 3.84×10¹⁴ Hz | - | - | - |
| 5. | Infra-Red waves | William Herschel | (a) Rearrangement of outer orbitals electrons in atoms and molecules (b) Change of molecular vibrational and rotational energies (c) By bodies at high temperature |
7.8×10⁻⁷ m to 10⁻³ m | 4×10¹⁴ Hz to 3×10¹¹ Hz | 1.6 eV to 1.6×10⁻³ eV | (a) Thermal effect (b) All properties similar to those of light except wavelength |
(a) Used in industry, medicine and astronomy (b) Used for fog or have photography |
| 6. | Microwaves | Hertz | Special electronic devices such as klystron tube | 10⁻³ m to 0.3m | 3×10¹¹ Hz to 10⁹ Hz | 10⁻³eV to 10⁻⁵eV | (a) Phenomena of reflection, refraction and diffraction | (a) Radar and telecommunication (b) Analysis of fine details of molecular structure |
| 7. | Radio waves | Marconi | Oscillating circuits | 0.3m to few kms | 10⁹ Hz to few Hz | 10⁻³eV to 0 | (a) Exhibit wave like properties more than particle like properties | (a) Radio communication (b) Radar, Radio and satellite communication (Microwaves) |
Subparts of Radio spectrum
| Type | Wavelength | Frequency | Applications |
|---|---|---|---|
| (a) Super High (SHF) | 0.01m to 0.1m | 3×10¹⁰ Hz to 3×10⁹ Hz | Radar and television broadcast |
| (b) Ultra High (UHF) | 0.1m to 1m | 3×10⁹ Hz to 3×10⁸ Hz | Short distance communication |
| (c) Very High (VHF) | 1m to 10m | 3×10⁸ Hz to 3×10⁷ Hz | Television communication |
| High frequency | 10m to 100m | 3×10⁷ Hz to 3×10⁶ Hz | Medium distance communication |
| Medium frequency | 100m to 1000m | 3×10⁶ Hz to 3×10⁵ Hz | Marine and navigation use |
| Low Frequency | 1000m to 10000m | 3×10⁵ Hz to 3×10⁴ Hz | Long range communication |
| Very low frequency | 10000m to 30000m | 3×10⁴ Hz to 10³ Hz | Long distance communication |
EARTH'S ATMOSPHERE AND ELECTROMAGNETIC WAVES
(i) Earth's Atmosphere
The gaseous envelop surrounding the earth is called earth's atmosphere.
(ii) Composition
It mainly consists of nitrogen 78% and oxygen 21% alongwith a little portion of argon, carbon-di-oxide, water vapour, hydrocarbons, sulphur compounds and dust particles.
(iii) Density Variation
The density of atmospheric air goes on decreasing gradually as we go up.
(iv) Atmospheric Layers
The earth's atmosphere has no sharp boundary. However, it has been divided into various regions as given below:
- (a) Troposphere
It extends upto a height of 12 km from earth's surface. The temperature in this region decreases from 298K to 220K and conductivity increases. All climatic changes occur in this region.
- (b) Stratosphere
It extends from 12 km to 50 km after troposphere. At the upper part of this region, approximately 20km thick, most of ozone of atmosphere is concentrated. This layer is called as ozone layer. This layer absorbs very large portion of ultraviolet radiations coming from sun, therefore its temperature increases from 220K to 280K.
- (c) Mesosphere
It extends from 50km to 80 km after stratosphere. In this region the temperature decreases from 280K to 180K
- (d) Ionosphere
It extends from 80 km to 400 km after mesosphere. The temperature of this region rises from 180K to 700K. In this region ultraviolet radiation coming from sun cause ionisation, therefore this part mostly consists of free electrons and positive ions. The concentration of free electrons is found to be very large in a region beyond 110 km from earth's surface which extends vertically for a few kilometers and is called Kennelly Heaviside layer. Beyond this layer the concentration of free electrons decreases considerably until a height of about 250 km. Beyond it there is another layer of electrons, called Appleton layer.
(v) Greenhouse Effect
The atmosphere is transparent to visible radiations, but most infrared (heat) radiations are not allowed to pass through. The energy from the sun heats the earth which then starts emitting radiations like any other hot body. However, since the earth is much colder than sun, its radiations are mainly in the infra red region. These radiations are unable to cross the lower atmosphere and are reflected back. Low lying clouds also reflect back the infra red radiations. As such, the earth's surface warm at night. This phenomenon is called the Green house effect.
(vi) Propagation of Radio waves
- (a) Low frequency waves - the AM band
Radio waves having wavelengths of 10m or more (frequency less than 30 MHz) are said to constitute the AM band. The lower atmosphere is transparent to these waves, but the ionosphere reflects them back. A signal transmitted from a certain point can be received at another point in two possible ways - directly along the surface of the earth (called ground wave) and after reflection from ionosphere (called sky wave). Waves having frequencies upto about 1500kHz (Wavelength above 200m) are mainly transmitted through ground because low frequency sky waves lose their energy very quickly than the sky waves. Therefore, higher frequencies are mainly transmitted through sky. These two regions of the AM band are called medium wave and short wave bands respectively.
- (b) High frequency waves - Television transmission
Above a frequency of about 40MHz the ionosphere does not reflect the wave toward the earth. The television signals have frequencies in the range 100-200 MHz. Therefore TV transmission via the sky is not possible - only direct reception via the ground is possible. Therefore, in order to have larger coverage, the transmission has to be done through very tall antennas. The height of transmitting antenna for TV telecast is given by
h = d2/(2Re)
where d is the radius of the area to be covered for TV telecast and Re is the radius of earth.
Illustration 8: A T.V. tower has a height of 100m. How much population is covered by T.V. broadcast, if the average population density around the tower is 1000/km²?
Options:
(A) 39.5 × 105
(B) 19.5 × 106
(C) 29.5 × 107
(D) 9 × 104
Solution:
(A) Radius of the area covered by T.V. telecast
d = √(2hRe)
Total population covered = πd² × population density
= 2πhRe × population density = 2 × 3.14 × 100 × 6.4 × 10⁶ × (1000/10⁶) = 39.503 × 10⁵
Illustration 9: An electromagnetic radiation has an energy 14.4 KeV. To which region of electromagnetic spectrum does it belong?
Options:
(A) Infra red region
(B) Visible region
(C) X-ray region
(D) Y-ray region
Solution:
Frequently Asked Questions
Electromagnetic waves are a type of energy that travels through space by combining electric and magnetic fields. Imagine a ripple in water except, instead of water moving, it’s electric and magnetic fields interacting. These fields vibrate at right angles to each other and to the direction in which the wave travels. Because of this, electromagnetic waves are classified as transverse waves.
One of the most important aspects of electromagnetic waves is that they do not need a medium like air, water, or solid material to travel. This means they can move through the vacuum of space, which is why sunlight reaches Earth even though space is nearly empty.
Electromagnetic waves cover a broad spectrum known as the electromagnetic spectrum, ranging from very long-wavelength radio waves to very short-wavelength gamma rays. In between, we find microwaves, infrared, visible light, ultraviolet, and X-rays. Each type carries energy, interacts with matter differently, and has unique applications.
For example:
- Radio waves are used in communication systems like radio, television, and Wi-Fi.
- Microwaves are used in radar and cooking.
- Visible light allows us to see.
- X-rays are used in medical imaging.
The speed of electromagnetic waves in a vacuum is the universal constant known as the speed of light, approximately 3 × 10^8 meters per second.
To simplify: electromagnetic waves are “energy in motion,” created whenever electric charges accelerate. When you switch on a lightbulb, the electrons in the filament accelerate and generate electromagnetic waves—some of which fall into the visible spectrum, letting you see light.
Understanding this concept helps in everything from daily life (using your phone, which relies on radio waves) to advanced fields like astronomy, medical imaging, and wireless communication. At its core, an electromagnetic wave is the messenger of energy moving seamlessly across the universe.
Think of electromagnetic waves as a dance between two invisible partners: electricity and magnetism. Each one constantly creates and influences the other, resulting in a self-sustaining wave that can travel through space without needing air or material.
Here’s the breakdown:
- The electric field (E-field) oscillates up and down.
- The magnetic field (B-field) oscillates sideways.
- Together, they move forward at the speed of light.
This pairing is why we call them “electromagnetic” waves.
Everyday life is full of examples of these waves. When you use a remote control, it sends infrared electromagnetic waves. Your Wi-Fi router uses radio waves. When you step into sunlight, you are bathed in electromagnetic radiation across several parts of the spectrum, including visible light and ultraviolet.
The reason they are so important is that electromagnetic waves are how energy and information are transmitted across vast distances. Without them, there would be no wireless communication, no vision, and no way to detect the universe around us.
To truly visualize it: imagine holding a rope and wiggling one end up and down. Waves travel along the rope, but in EM waves, instead of rope, it’s electric and magnetic fields creating ripples through space.
So, electromagnetic waves are not just abstract physics—they are the backbone of modern technology and the universe itself. Understanding them is the foundation for grasping how we see, communicate, and interact with the world.
Imagine you have two friends, one always pulling upward and downward, and the other pulling side to side. They take turns so quickly that together they push something forward without ever letting it stop. That’s how electromagnetic waves work electric fields go up and down, magnetic fields go side to side, and together they push energy forward through space.
Unlike sound waves that need air or water to move, electromagnetic waves can travel through empty space. That’s why light from the Sun reaches Earth across 150 million kilometers of vacuum.
Every color you see is actually part of the electromagnetic spectrum. Red light has a longer wavelength, while blue light has a shorter wavelength. Beyond what we can see, there are waves like microwaves, X-rays, and gamma rays, all working under the same principle.
Why does this matter for learners? Because once you grasp this simple model, you can connect it to real-world experiences:
- Microwave oven: uses microwaves (a type of EM wave) to heat food.
- Sunburn: ultraviolet rays (another EM wave) cause skin reactions.
- Radio: your favorite station is transmitted using radio waves.
In short: an electromagnetic wave is just energy traveling through space, created by wiggling electric charges, moving at the speed of light, and forming the foundation of communication, vision, and modern life.
Electromagnetic waves are disturbances formed by the interaction of electric and magnetic fields. These fields oscillate perpendicular to each other and also perpendicular to the direction of wave travel, which makes electromagnetic waves a perfect example of transverse waves. They are not confined to one type of energy, instead, they combine two: the electric field and the magnetic field.
Unlike mechanical waves such as sound or water ripples, electromagnetic waves do not require a medium. They can propagate through a vacuum, which explains how sunlight and starlight reach us across vast interstellar space. Their ability to travel independently of matter makes them essential for energy transfer across the universe.
The collection of all possible electromagnetic waves is called the electromagnetic spectrum. This spectrum spans radio waves (with the longest wavelength and lowest frequency) to gamma rays (with the shortest wavelength and highest frequency). Between these two extremes lie microwaves, infrared radiation, visible light, ultraviolet rays, and X-rays. Each portion of the spectrum plays a role in everyday life. For example, visible light enables human vision, infrared is used in remote controls, and X-rays are vital in medical imaging.
The defining characteristics of electromagnetic waves are their wavelength, frequency, and speed. In a vacuum, they all travel at the same constant speed, the speed of light (c = 3 × 10^8 m/s). The energy carried by an electromagnetic wave depends on its frequency: higher frequency means higher energy.
In simple terms, electromagnetic waves are the universal carriers of energy and information. Without them, life as we know it would not exist there would be no sunlight to sustain ecosystems, no radio or internet, and no medical tools for diagnostics. Understanding the general definition provides a foundation for learning their behavior, applications, and importance in science and technology.
In physics, an electromagnetic wave is defined as a self-propagating transverse wave of oscillating electric and magnetic fields that moves through space at the speed of light. This definition highlights three critical aspects:
- Self-propagating nature: The changing electric field generates a magnetic field, and the changing magnetic field, in turn, regenerates the electric field. This mutual generation sustains the wave’s motion even in the absence of a physical medium.
- Transverse orientation: Both fields oscillate at right angles to each other and to the direction of wave travel. If the wave moves in the x-direction, the electric field might oscillate in the y-direction, and the magnetic field in the z-direction.
- Speed of propagation: In a vacuum, electromagnetic waves move at the universal constant, the speed of light. Their velocity in matter varies depending on the material’s optical density.
The mathematical foundation of this definition comes from Maxwell’s equations, which unify electricity and magnetism into a single framework. These equations predict the existence of electromagnetic waves and describe their propagation.
For learners, it is helpful to connect this definition with real-world examples. The light we see is an electromagnetic wave with wavelengths between 400 and 700 nanometers. Your mobile phone uses radio-frequency electromagnetic waves to communicate with towers. Even microwave ovens operate by exciting water molecules with microwaves.
This precise definition ensures scientific clarity and provides the stepping stone to more advanced study, such as quantum electrodynamics, where electromagnetic waves are described in terms of photons, the particles of light.
Magnetic waves and electromagnetic waves are often confused, but the distinction lies in context.
- A magnetic wave refers to the oscillating magnetic component of a wave. By itself, a magnetic wave cannot exist independently in space it is always paired with an electric field when propagating.
- An electromagnetic wave, on the other hand, is the full phenomenon of a self-sustaining combination of oscillating electric and magnetic fields.
In every electromagnetic wave, the magnetic field and electric field are interlinked. If you imagine the wave traveling forward, the electric field oscillates up and down, while the magnetic field oscillates side to side. These fields are in phase, meaning they reach their peaks and troughs at the same points in space and time.
The term “magnetic waves” sometimes comes up in discussions of magnetohydrodynamics or plasma physics, where disturbances in a magnetic field within a conducting fluid can behave like waves. However, in the context of general physics and electromagnetic theory, we treat electromagnetic waves as the complete system.
Electromagnetic waves manifest in a wide variety of ways:
- Radio waves transmit information across continents.
- Infrared radiation provides heat.
- Visible light allows us to see.
- Ultraviolet and X-rays carry higher energies useful in scientific and medical contexts.
Understanding the relationship between magnetic and electromagnetic waves clarifies that magnetism is not separate from electromagnetic theory but is part of a broader, unified phenomenon. Without both electric and magnetic fields working in harmony, electromagnetic waves could not exist.
Electromagnetic waves propagate because of the dynamic interplay between electric and magnetic fields. A changing electric field produces a magnetic field, and a changing magnetic field produces an electric field. This mutual regeneration means that once initiated, the wave can carry itself forward through space without any external support.
To picture it intuitively, think of a “relay race” between electricity and magnetism. The electric field hands energy to the magnetic field, which then passes it back to the electric field, and this cycle continues endlessly. Together, they form a self-sustaining system that moves forward at the speed of light.
From a physics perspective, this is a direct consequence of Maxwell’s equations. These four fundamental laws describe how electric and magnetic fields interact. When solved in free space, they predict a wave that propagates at a speed exactly equal to the speed of light, proving that light itself is an electromagnetic phenomenon.
In everyday terms, imagine wiggling one end of a rope. That wiggle travels down the rope because energy is transferred through the rope’s structure. With electromagnetic waves, the medium isn’t matter—it’s the fields themselves. Once an oscillating charge produces a disturbance, the fields sustain and carry that energy across space.
This mechanism explains why we can receive radio signals from distant towers, see starlight that has traveled for millions of years, and use devices like Wi-Fi routers without wires. Each example is powered by the natural propagation of electromagnetic waves.
Electromagnetic waves propagate because electric and magnetic fields are coupled in such a way that one always regenerates the other, allowing energy to move seamlessly through space.
When electromagnetic waves travel through matter, they interact with the material’s electrons and atoms. This interaction determines how the wave behaves whether it passes through, slows down, reflects, or gets absorbed.
The speed of electromagnetic waves in matter is generally slower than in a vacuum. This slowdown is described by the material’s refractive index. For example, light travels more slowly in water or glass than in air, which is why objects underwater appear bent or displaced.
Here’s the process in simple terms:
- The oscillating electric field of the wave causes charged particles (like electrons) in the material to vibrate.
- These vibrations create new electromagnetic disturbances, which combine with the original wave.
- The result is a delayed and sometimes weakened wave traveling through the material.
The degree of absorption or transmission depends on the wave’s frequency. For instance, visible light passes easily through glass, while ultraviolet is absorbed. Radio waves penetrate walls, but X-rays can pass through soft tissue while being absorbed by bones.
In conductive materials like metals, free electrons absorb the wave’s energy and re-emit it, causing strong reflection. That’s why metals are shiny and block most electromagnetic waves.
This behavior of EM waves in matter is the foundation of technologies like:
- Fiber optics (light traveling through glass with minimal loss).
- Medical imaging (X-rays passing through tissue but not bone).
- Solar panels (absorbing sunlight and converting it to electricity).
In summary, electromagnetic waves travel through matter by interacting with charged particles, and the outcome refraction, absorption, transmission, or reflection depends on the material and the wave’s frequency.
Electromagnetic waves are often depicted as moving electric and magnetic fields because this visualization directly represents their true physical structure. A wave is not just abstract energy it is a coordinated oscillation of two fields:
- The electric field (E-field) oscillates in one direction.
- The magnetic field (B-field) oscillates perpendicular to the electric field.
- Both are perpendicular to the wave’s direction of motion.
This creates the classic three-dimensional picture: if the wave travels along the x-axis, the electric field vibrates along the y-axis, and the magnetic field along the z-axis.
These depictions are not arbitrary—they are derived from Maxwell’s equations. The math shows that any oscillating electric field produces a perpendicular magnetic field, and vice versa. Together, they form a transverse wave that carries energy.
The reason these diagrams are so important in teaching is that they show learners why EM waves can sustain themselves. Unlike sound waves, which compress and expand particles in a medium, EM waves are fields generating each other. The moving fields are the very mechanism of propagation.
Visualizing them also helps explain polarization, wave speed, and the relationship between wavelength and frequency. For example, polarized sunglasses block light with electric fields oscillating in one direction. This makes the wave diagrams directly relevant to practical life.
In conclusion, electromagnetic waves are depicted as moving electric and magnetic fields because that is precisely what they are—self-sustaining oscillations of fields, each perpendicular to the other, moving forward as energy at the speed of light.
All electromagnetic waves travel at the same speed in a vacuum the speed of light (c ≈ 3 × 10^8 m/s)—because this velocity is determined by the fundamental properties of space itself, not by the wave’s frequency or energy.
According to Maxwell’s equations, the speed of an electromagnetic wave in a vacuum depends on two constants:
- The permittivity of free space (ε₀), which measures how electric fields interact in a vacuum.
- The permeability of free space (μ₀), which measures how magnetic fields interact in a vacuum.
The relationship is:
c=1/√μ0ε0
This shows that the speed is fixed by nature’s constants. It doesn’t matter whether the wave is a low-frequency radio wave or a high-frequency gamma ray—they all propagate at the same speed in empty space.
This principle explains why light from stars and galaxies reaches us after traveling millions of years regardless of whether it’s visible light or X-rays, the speed is the same.
However, once electromagnetic waves enter a medium (like air, water, or glass), their speed changes. Different frequencies can slow down differently, leading to dispersion effects, such as the rainbow formed when white light passes through a prism. But in the absence of matter, all EM waves share the same constant velocity.
The constancy of this speed was revolutionary. It underpinned Einstein’s theory of relativity, which made the speed of light the ultimate speed limit of the universe.
In short: electromagnetic waves have the same speed in a vacuum because they are governed by the intrinsic properties of space itself. Their speed is a universal constant that defines the very structure of physics.
The statement highlights the distinction between the wave model and the particle model of light.
Electromagnetic waves can be described in two complementary ways:
- Wave model: Light behaves like a continuous wave with oscillating electric and magnetic fields. This explains interference, diffraction, and polarization.
- Particle model: Light also behaves as packets of energy called photons. Each photon has an energy proportional to its frequency, given by Planck’s equation: E=hf
where E is energy, h is Planck’s constant, and f is frequency.
All photons are manifestations of electromagnetic waves at the quantum level. A photon is essentially the smallest unit (quantum) of an electromagnetic wave. However, not all electromagnetic waves are conveniently described at the photon level, especially when considering large-scale, low-energy waves like radio transmissions. In those cases, the wave description is more practical.
The phrase “not all waves are photons” reminds us that waves in general such as sound waves or water waves—are not photons at all. Photons are specific to electromagnetic radiation.
Understanding this duality helps learners appreciate modern physics. Technologies like lasers, solar panels, and quantum computing rely on treating light as photons. On the other hand, radio antennas and optical lenses are better understood with wave theory.
Thus, photons and electromagnetic waves are two sides of the same coin: photons describe the particle nature of EM waves, while wave theory explains their continuous properties. Together, they provide a complete picture of light and radiation.
It’s true that electromagnetic waves have no rest mass, but they still carry energy and momentum. This is possible because energy in physics is not limited to mass it can also be stored and transmitted in fields.
An electromagnetic wave consists of oscillating electric and magnetic fields. These fields store energy in two ways:
- Electric field energy density: proportional to the square of the electric field strength.
- Magnetic field energy density: proportional to the square of the magnetic field strength.
Together, they form the energy density of the wave. The energy is transported as the wave propagates, carried in the form of the Poynting vector, which represents the directional flow of electromagnetic energy.
S=μ0 1 (E×B)
This equation shows that the cross product of electric and magnetic fields gives the energy flow direction and magnitude.
Even though photons (the quantum particles of EM waves) have no rest mass, they do have energy and momentum. Einstein’s famous relation E = mc^2
E=mc2 links mass and energy, but photons follow the quantum relation:
E=hf, p= E/c
where E is energy, p is momentum, h is Planck’s constant, and f is frequency.
This explains phenomena like solar sails, where spacecraft can be propelled by sunlight. Though photons are massless, their momentum transfer is enough to push an object in space.
Thus, electromagnetic waves carry energy because their oscillating fields transport it, and photons, though massless, embody energy and momentum. This duality makes EM radiation one of the most powerful carriers of energy across the universe.