1. Basic nature of electromagnetic waves
Electromagnetic waves are disturbances in electric and magnetic fields. These fields vary with time and travel through space, carrying energy from one point to another.
The key idea is that an electromagnetic wave is made of two oscillating fields: an electric field and a magnetic field. Both fields support each other and form a self-sustaining wave.
1.1. Linked electric and magnetic fields
The electric field \(\vec{E}\) changes with time, and this change creates a changing magnetic field \(\vec{B}\). At the same time, the changing magnetic field creates a changing electric field. This continuous process allows the wave to propagate forward.
1.2. Self-sustaining propagation
Once formed, the wave does not need any further charges or currents to keep moving. The changing fields generate each other, making the wave self-sustaining as it travels through space.
2. Electromagnetic waves are transverse waves
Electromagnetic waves are fundamentally transverse. This means the oscillations of the electric and magnetic fields take place at right angles to the direction of propagation of the wave.
2.1. Perpendicular orientation of fields
If the wave is travelling along the x-axis, the electric field may oscillate along the y-axis and the magnetic field along the z-axis. All three directions are perpendicular to each other.
2.1.1. Mathematical representation
\(\vec{E} \perp \vec{B}, \quad \vec{E} \perp \vec{k}, \quad \vec{B} \perp \vec{k}\)
where \(\vec{k}\) is the direction of propagation of the wave.
2.2. Wave behaviour linked to field directions
Because the fields oscillate perpendicular to the motion of the wave, the wave can be polarised. This is a key feature of transverse waves and is one of the strongest proofs that light is an electromagnetic wave.
3. Creation of electromagnetic waves
An electromagnetic wave is produced whenever an electric charge accelerates. This could be due to a change in speed or direction.
3.1. Accelerating charges
A charge moving at constant speed creates steady electric and magnetic fields. When the charge accelerates, these fields cannot adjust instantly everywhere, so the disturbance in the fields moves outward in all directions as an electromagnetic wave.
3.2. Changing electric field creating magnetic field
A time-varying electric field gives rise to a time-varying magnetic field. Maxwell added this idea to Ampère's law, completing the symmetry between electricity and magnetism.
3.3. Changing magnetic field creating electric field
Similarly, Faraday discovered that a changing magnetic field induces an electric field. Together, these two processes allow the disturbance to detach from the source and travel independently as a wave.
4. Mathematical description of an electromagnetic wave
The electric and magnetic fields in a simple travelling wave can be represented using sinusoidal functions. These fields oscillate in space and time and move with the same phase and speed.
4.1. Electric field expression
\(E_y(x,t) = E_0 \sin(kx - \omega t)\)
This shows an electric field pointing along the y-axis and varying with position and time.
4.2. Magnetic field expression
\(B_z(x,t) = B_0 \sin(kx - \omega t)\)
The magnetic field oscillates along the z-axis with the same frequency and phase as the electric field.
4.3. Relation between field amplitudes
In an electromagnetic wave, the magnitudes of the electric and magnetic fields are related by:
\(\dfrac{E_0}{B_0} = c\)
This shows that the electric field magnitude is much larger than the magnetic field magnitude because the speed of light \(c\) is very large.
5. Propagation without a medium
Electromagnetic waves do not need a material medium to travel. They can move through air, glass, water, and even perfect vacuum.
5.1. Fields exist even in empty space
Electric and magnetic fields do not need matter to exist. They can exist independently in space. So the oscillations of these fields form waves that travel freely without any physical medium.
5.2. Why mechanical waves cannot do this
Mechanical waves need particles of a medium to oscillate, which is why sound cannot travel through vacuum. But electromagnetic waves rely only on fields, not matter.
6. Energy transfer in electromagnetic waves
Electromagnetic waves carry energy. This is how energy from the Sun reaches Earth, even though the space between is almost a perfect vacuum.
6.1. Energy in the electric and magnetic fields
The oscillating electric and magnetic fields both store energy. In a plane wave, the energy is equally shared between the two fields.
6.2. Intensity of the wave
The intensity is the amount of energy delivered per unit area per unit time. It depends on the square of the amplitudes of the electric and magnetic fields.
\(I \propto E_0^2\)