Electromagnetic Waves Overview

A change in the magnetic flux surrounding a conductor produces an electromotive force (EMF) in the conductor.

The phenomenon where a changing electric field generates a magnetic field.

A type of current that is generated solely due to a changing electric field in a region of space (like in vacuum or free space).

The current that flows through a conductor due to the movement of free charges.

The principle that the total current passing through a closed loop is equal to the sum of the conduction current and the displacement current.

A current due to a changing electric field in space, contributing to the generation of a magnetic field.

The property that the total current entering a region is equal to the total current leaving that region.

A moving charged particle creates a magnetic field around it.

When a charged particle accelerates, it emits electromagnetic waves, which are disturbances that propagate through space.

An oscillating electric field produces an oscillating magnetic field, and vice versa. These oscillations are synchronized and travel together as an electromagnetic wave.

Electromagnetic waves are transverse waves, meaning that the electric and magnetic fields oscillate perpendicular to the direction of wave propagation.

An electromagnetic wave is characterized by its electric field (E) and magnetic field (B) components. The electric field is given by E = E0sin(kx - ωt) and the magnetic field is given by B = B0sin(kx - ωt), where E0 and B0 are the amplitudes, k is the wave number, ω is the angular frequency, and t is time. These equations describe the sinusoidal variation of the fields as the wave propagates.

A traveling wave is a disturbance that propagates through space or a medium. It can be described by a mathematical function that describes the displacement of a particle as a function of position and time.

The displacement of a particle in a traveling wave can be represented by the equation y = A sin(kx - ωt), where A is the amplitude, k is the wave number, ω is the angular frequency, and t is time.

Electromagnetic waves are produced by oscillating charges and travel through space at the speed of light. These waves consist of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of wave propagation.

The direction of energy flow per unit area per unit time along the direction of wave propagation.

Electromagnetic waves are produced by accelerated charges and do not require any material medium for their propagation. They are transverse in nature because the oscillations of the electric (E) and magnetic (B) fields are perpendicular to each other and to the direction of wave propagation. Furthermore, the oscillations of E and B fields are in the same phase.

All electromagnetic waves travel in free space with the same speed, c = (1/√(μ₀ε₀)) ≈ 3 x 10⁸ m/s. In a material medium, their speed is given by v = c/√(με) = c/√(μᵣεᵣ) = c/n, where n is the refractive index of the medium.

The amplitude ratio of the electric and magnetic fields is E₀/B₀ = c = √(μ₀ε₀). Electromagnetic waves carry energy as they travel through space, and this energy is shared equally by the electric and magnetic fields.

The electromagnetic waves transport linear momentum as they travel through space, given by p = U/c, where U is the energy of the wave. Electromagnetic waves obey the principle of superposition.

The energy stored per unit volume in an electric field.

The energy stored per unit volume in a magnetic field.

The average energy density of an electromagnetic wave is the sum of the average energy densities of the electric and magnetic fields.

The energy transferred per unit area per unit time by an electromagnetic wave.

The energy stored per unit volume in an electric field is equal to 1/2 * ε₀ * E₀².

The energy stored per unit volume in a magnetic field is equal to 1/2 * B₀² / μ₀.

The average energy density of the electric field is equal to the average energy density of the magnetic field.

The average energy density of an electromagnetic wave is given by 1/2 * ε₀ * E₀² or equivalently, 1/2 * B₀² / μ₀.

The energy stored in an electric field is associated with the capacitor.

The energy stored in a magnetic field is associated with the inductor.

The direction of propagation of an electromagnetic wave is perpendicular to both the electric field and the magnetic field. It can be determined using the right-hand rule: point your fingers in the direction of the electric field, curl them towards the magnetic field, and your thumb will point in the direction of propagation. A simple way to remember this is: Electric, B magnetic, Propagation, E × B = P.

The speed of an electromagnetic wave in a vacuum is the speed of light, approximately 3 × 10⁸ m/s. This speed is determined by the permittivity and permeability of free space, and is a fundamental constant of nature.

The peak value of the electric field (Eo) is the maximum value of the electric field strength in an electromagnetic wave. It is directly proportional to the amplitude of the wave, meaning a higher Eo indicates a stronger wave. Similarly, the peak value of the magnetic field (Bo) is the maximum value of the magnetic field strength.

The relationship between the electric field and magnetic field in an electromagnetic wave is given by the equation E = cB, where c is the speed of light. This means that the magnitudes of the electric and magnetic fields are connected by a constant factor, and both oscillate in phase.

The permeability of a medium is a measure of how easily it can be magnetized. Free space has a permeability of μ₀, which is a constant. The relative permeability μr is the ratio of the permeability of a material to the permeability of free space. A material with a high permeability will have a large μr.

The permittivity of a medium is a measure of how easily it can be polarized by an electric field. Free space has a permittivity of ε₀, which is a constant. The relative permittivity (dielectric constant) K is the ratio of the permittivity of a material to the permittivity of free space. A material with a high permittivity will have a large K.

The speed of an electromagnetic wave in a medium is determined by the permeability and permittivity of the medium. The formula for the speed in a medium is v = c/√(μrK), where c is the speed of light in vacuum, μr is the relative permeability, and K is the dielectric constant.

The energy density of an electromagnetic wave is the amount of energy stored per unit volume of the wave. It is given by U = (1/2)ε₀E² + (1/2)(1/μ₀)B². This shows that the energy is equally distributed between the electric and magnetic fields.

Intensity is the power per unit area of the electromagnetic wave, which is a measure of the energy flow through a surface. It is given by I = (1/2)cε₀E², where c is the speed of light and ε₀ is the permittivity of free space.

Electromagnetic waves carry momentum. The momentum density is given by p/V = (U/c), where U is the energy density and c is the speed of light. This means that momentum is also proportional to the energy density of the wave.