Key Points

James Clerk Maxwell proposed that a changing electric field produces a magnetic field, which is the converse of Faraday's law of induction. This idea is fundamental to the existence of electromagnetic waves.

Displacement current ($i_d$) is a current that exists due to a time-varying electric field. It is given by the formula $i_d = \varepsilon_0 \frac{d\Phi_E}{dt}$, where $\Phi_E$ is the electric flux.

This is the modified form of Ampere's circuital law that includes displacement current. The law is stated as $\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 (i_c + i_d) = \mu_0 i_c + \mu_0 \varepsilon_0 \frac{d\Phi_E}{dt}$.

These four equations (Gauss's Law for electricity, Gauss's Law for magnetism, Faraday's Law, and Ampere-Maxwell Law) form the complete basis of classical electromagnetism.

Electromagnetic (EM) waves are produced by accelerated electric charges. An oscillating charge is a primary example of a source that radiates EM waves.

EM waves are transverse in nature. The oscillating electric field vector (E), magnetic field vector (B), and the direction of wave propagation are all mutually perpendicular.

EM waves are self-sustaining oscillations of electric and magnetic fields that do not require a material medium for propagation. They travel through vacuum and carry energy and momentum.

In vacuum, all EM waves travel at the speed of light, c, which is a fundamental constant. It is given by $c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \approx 3 \times 10^8 \text{ m/s}$.

In a material medium with absolute permittivity $\varepsilon$ and absolute permeability $\mu$, the speed of EM waves is reduced to $v = \frac{1}{\sqrt{\mu \varepsilon}}$.

The amplitudes of the electric field ($E_0$) and magnetic field ($B_0$) in an EM wave are related. In vacuum, the relationship is $E_0 = cB_0$.

For a plane EM wave traveling along the z-axis, the fields can be represented sinusoidally as $E_x = E_0 \sin(kz - \omega t)$ and $B_y = B_0 \sin(kz - \omega t)$.

The speed of an EM wave is related to its frequency ($\nu$) and wavelength ($\lambda$) by $c = \nu \lambda$. The angular frequency is $\omega = 2\pi\nu$ and the wave number is $k = \frac{2\pi}{\lambda}$.

The electromagnetic spectrum is the continuous range of all possible frequencies of electromagnetic radiation. Waves are classified into different types based on their frequency or wavelength.

In order of decreasing wavelength (increasing frequency and energy), the spectrum includes: Radio waves, Microwaves, Infrared, Visible light, Ultraviolet, X-rays, and Gamma rays.

Radio waves are produced by oscillating charges in conducting wires and are used in communication. Microwaves are used in radar systems and for heating in microwave ovens.

Infrared waves are produced by hot bodies and are associated with heat. Visible light is the narrow part of the spectrum that the human eye can detect.

Ultraviolet (UV) rays can cause skin tanning and are used for sterilization. X-rays are used for medical imaging, and Gamma rays, having the highest energy, are used in radiotherapy to destroy cancer cells.