1. What are electromagnetic waves?
Electromagnetic waves are waves made of two linked fields: an electric field and a magnetic field. These two fields keep changing with time and help each other to move forward through space.
Unlike sound waves in air or water waves on the surface of a pond, electromagnetic waves do not need any material medium. They can travel even through empty space (vacuum).
1.1. Basic idea in simple words
Imagine a region where the electric field is changing with time. This changing electric field creates a changing magnetic field around it. In turn, this changing magnetic field creates a changing electric field again. This chain continues and the disturbance moves forward through space as a wave.
So an electromagnetic wave is basically a self-sustaining combination of electric and magnetic fields, spreading out from the source.
1.2. Everyday examples of electromagnetic waves
- Light from a bulb or the Sun
- Radio and TV signals
- Wi-Fi and mobile signals
- Microwave oven radiation
- Infrared radiation used in remote controls
All of these are different forms of electromagnetic waves with different frequencies and wavelengths.
2. Definition of electromagnetic waves
Definition: An electromagnetic wave is a wave in which the electric field \(\vec{E}\) and the magnetic field \(\vec{B}\) vary with time and space, are mutually perpendicular, and together propagate through space, even in vacuum.
In a simple case, both fields oscillate sinusoidally and move in a fixed direction with speed \(c\) in vacuum.
3. How electromagnetic waves are produced
The root source of electromagnetic waves is an accelerating charge. Whenever charge moves in such a way that its velocity changes with time, it disturbs the surrounding electric and magnetic fields and this disturbance can detach and travel away as an electromagnetic wave.
3.1. Accelerating charges
A charge at rest produces only an electric field around it. A charge moving with constant speed produces an electric field and a magnetic field that are steady in time.
When the charge is accelerated (speed or direction of motion is changing), the electric and magnetic fields also change with time. This time-varying field pattern spreads outward as an electromagnetic wave.
3.2. Changing electric and magnetic fields
A key idea is:
- A changing electric field produces a changing magnetic field.
- A changing magnetic field produces a changing electric field.
This mutual production allows the disturbance to keep moving without needing charges everywhere in space.
3.3. Self-sustaining nature of the wave
Once formed, the electromagnetic wave becomes self-sustaining:
- The changing electric field at one point generates a changing magnetic field nearby.
- That changing magnetic field again generates a changing electric field slightly ahead.
- This chain continues and the wave front moves forward.
3.3.1. Maxwell's picture
Maxwell combined the laws of electricity and magnetism and showed mathematically that a changing electric field and a changing magnetic field can together satisfy a wave equation. The solution of this wave equation predicts waves that travel with speed
\(c = \dfrac{1}{\sqrt{\mu_0\,\varepsilon_0}}\)
where \(\mu_0\) is the permeability and \(\varepsilon_0\) is the permittivity of free space. Numerically,
\(c \approx 3 \times 10^8\, \text{m s}^{-1}\)
which matches the measured speed of light. This is why light is understood as an electromagnetic wave.
4. Properties of electromagnetic waves
Electromagnetic waves have some key properties which make them different from mechanical waves like sound waves or water waves.
4.1. Transverse nature
In an electromagnetic wave, the electric field \(\vec{E}\) and magnetic field \(\vec{B}\) are both transverse to the direction of propagation:
- \(\vec{E}\) is perpendicular to the direction of motion of the wave.
- \(\vec{B}\) is also perpendicular to the direction of motion.
- \(\vec{E}\) is perpendicular to \(\vec{B}\) as well.
So \(\vec{E}\), \(\vec{B}\), and the direction of propagation form a mutually perpendicular triad.
4.2. Speed in vacuum
In free space (vacuum), all electromagnetic waves travel with the same speed
\(c \approx 3 \times 10^8\, \text{m s}^{-1}\)
This is true whether the wave is radio, microwave, visible light, X-rays, or gamma rays. Only the frequency and wavelength differ.
4.2.1. Relation between speed, frequency and wavelength
For any wave, including electromagnetic waves,
\(v = f\,\lambda\)
In vacuum, \(v = c\), so
\(c = f\,\lambda\)
where:
- \(f\) is the frequency in hertz (Hz).
- \(\lambda\) is the wavelength in metre (m).
4.3. Direction of \(\vec{E}\), \(\vec{B}\) and propagation
If the wave is travelling along the +x direction, a simple picture is:
- Electric field \(\vec{E}\) oscillates along the y direction.
- Magnetic field \(\vec{B}\) oscillates along the z direction.
- The wave front moves along x.
This can be written compactly as:
\(\vec{E} \perp \vec{B},\; \vec{E} \perp \vec{k},\; \vec{B} \perp \vec{k}\)
where \(\vec{k}\) is the direction of propagation.
4.4. Need of medium?
Mechanical waves (like sound) need a material medium because they involve local motion of particles of that medium.
Electromagnetic waves are different. The disturbance is in the electric and magnetic fields themselves, which exist even in empty space. So electromagnetic waves can travel through vacuum and do not need a material medium like air, water, or solid.
5. Mathematical form of a simple electromagnetic wave
For a simple plane electromagnetic wave travelling along the x-axis, the electric and magnetic fields can be expressed as sinusoidal functions of position and time.
5.1. Electric field as a sine wave
One common form is:
\(E_y(x,t) = E_0 \sin(kx - \omega t)\)
Here:
- \(E_0\) is the amplitude of the electric field.
- \(k\) is the wave number \(k = \dfrac{2\pi}{\lambda}\).
- \(\omega\) is the angular frequency \(\omega = 2\pi f\).
- The field oscillates along y while the wave travels along x.
5.2. Magnetic field as a sine wave
The corresponding magnetic field is:
\(B_z(x,t) = B_0 \sin(kx - \omega t)\)
where \(B_0\) is the amplitude of the magnetic field and the field oscillates along z.
5.3. Relation between \(E_0\) and \(B_0\)
For an electromagnetic wave in vacuum, the amplitudes of the fields are related by
\(\dfrac{E_0}{B_0} = c\)
This means the electric field amplitude is much larger numerically than the magnetic field amplitude, because \(c\) is very large.
6. Electromagnetic spectrum: quick overview
The set of all possible electromagnetic waves arranged according to frequency or wavelength is called the electromagnetic spectrum. All of them are basically the same type of wave; only \(f\) and \(\lambda\) differ.
6.1. Order of the electromagnetic spectrum
From lowest frequency (longest wavelength) to highest frequency (shortest wavelength), the spectrum can be remembered as:
- Radio waves
- Microwaves
- Infrared
- Visible light
- Ultraviolet
- X-rays
- Gamma rays
6.2. Simple uses linked to each region
- Radio waves: communication (radio, TV, mobile signals)
- Microwaves: cooking in microwave ovens, radar
- Infrared: heat radiation, remote controls
- Visible: ordinary light that the eye can detect
- Ultraviolet: sterilisation and some chemical reactions
- X-rays: medical imaging
- Gamma rays: nuclear processes, high-energy astrophysical events
Though their uses differ, all of these are electromagnetic waves travelling with speed \(c\) in vacuum.
7. Energy and intensity of electromagnetic waves
Electromagnetic waves carry energy and can transfer it from one place to another. This is how energy from the Sun reaches Earth through empty space.
7.1. Energy in electric and magnetic fields
Both the electric and magnetic parts of the wave store energy. In a plane electromagnetic wave in vacuum, the energy is shared equally between the electric field and magnetic field.
As the wave passes through a region, it delivers energy to any charges or matter present there.
7.2. Intensity and average power flow (concept only)
The intensity of an electromagnetic wave is the energy crossing unit area per unit time, perpendicular to the direction of propagation.
Mathematically, the detailed expression involves the Poynting vector, but for simple understanding it is enough to remember that intensity is proportional to the square of the field amplitudes, for example
\(I \propto E_0^2\)
So if the amplitude of the electric field is doubled, the intensity becomes four times.
8. Why electromagnetic waves can travel in vacuum
One of the most important features of electromagnetic waves is their ability to travel through vacuum, without any material medium.
8.1. Comparison with mechanical waves
Mechanical waves, like sound waves or water waves, involve actual displacement of particles in a medium. Without particles, there is nothing to oscillate, so mechanical waves cannot travel.
8.2. Self-propagation of fields
Electromagnetic waves involve oscillating electric and magnetic fields, not oscillating matter. These fields can exist in empty space.
Because a changing electric field produces a changing magnetic field and a changing magnetic field produces a changing electric field, the disturbance moves forward by this mutual support, even when no material medium is present.
9. Simple examples and visual intuition
A few everyday situations can make the idea of electromagnetic waves feel more concrete.
9.1. Light from a bulb
When a bulb is switched on, charges in the filament or LED circuit accelerate due to alternating or changing currents. This produces electromagnetic waves in the visible range (and also infrared, etc.) which spread out in all directions. When these waves enter the eye, they produce the sensation of sight.
9.2. Radio signal from a transmitter
In a radio transmitter antenna, alternating current is fed at some radio frequency. The accelerating charges in the antenna generate electromagnetic waves of that frequency. These waves travel through the atmosphere and can even go through vacuum in space. A receiving antenna picks up a tiny part of this energy and converts it back into electrical signals.
9.3. Sunlight reaching Earth
The Sun emits a wide range of electromagnetic waves, including visible light, infrared, ultraviolet and more. These waves travel through the vacuum of space and reach Earth, bringing both light and energy. Without any air or medium in most of the path, the waves still propagate because they are carried by the electric and magnetic fields themselves.