Electromagnetic Wave Equations and Calculations - SS2 Physics Lesson Note
Electromagnetic wave equations describe the behaviour and properties of electromagnetic waves. The fundamental equations governing electromagnetic waves are Maxwell's equations, which were formulated by James Clerk Maxwell in the 19th century. These equations relate the electric and magnetic fields to their sources and describe how they propagate through space.
Maxwell's Equations:
Maxwell's equations consist of four equations that describe the behaviour of electric and magnetic fields:
a. Gauss's Law for Electric Fields: This equation states that the electric flux through a closed surface is proportional to the total electric charge enclosed within the surface.
b. Gauss's Law for Magnetic Fields: This equation states that the magnetic flux through a closed surface is always zero, indicating the absence of magnetic monopoles.
c. Faraday's Law of Electromagnetic Induction: This equation describes how a changing magnetic field induces an electric field. It states that the induced electromotive force (emf) in a closed loop is equal to the negative rate of change of magnetic flux through the loop.
d. Ampere-Maxwell Law: This equation relates the magnetic field to the electric current and the rate of change of electric flux. It states that the circulation of the magnetic field around a closed loop is equal to the sum of the electric current passing through the loop and the rate of change of electric flux through the loop.
Wave Equation:
From Maxwell's equations, we can derive the wave equation, which describes the propagation of electromagnetic waves through space. The wave equation for electric and magnetic fields is a second-order partial differential equation, and its solution represents the travelling nature of electromagnetic waves.
Wave Speed:
The speed at which electromagnetic waves propagate through a vacuum is denoted by the symbol "c" and is approximately equal to 3 x 108 metres per second. This speed is the same for all electromagnetic waves and is a fundamental constant in physics.
Waveform and Wavelength:
The waveform of an electromagnetic wave can be described by its wavelength (λ), which is the distance between two consecutive crests or troughs of the wave. The wavelength is inversely proportional to the frequency (f) of the wave, and the relationship is given by the equation λ = c / f.
Wave Frequency and Period:
The frequency of an electromagnetic wave is the number of complete cycles it undergoes per unit time and is measured in hertz (Hz). The period (T) of the wave is the time taken to complete one full cycle. The frequency and period of a wave are related by the equation
f = 1 / T.
Wave Amplitude and Intensity:
The amplitude of an electromagnetic wave represents the maximum displacement of the electric and magnetic fields from their equilibrium positions. It determines the wave's intensity, which is a measure of the energy carried by the wave per unit area per unit of time.
Wave Interference:
Electromagnetic waves can undergo interference when two or more waves overlap. Interference can be constructive, where the waves reinforce each other, or destructive, where they cancel each other out. The resulting interference pattern depends on the relative phase and amplitude of the interfering waves.
Calculations:
Various calculations can be performed using electromagnetic wave equations, including determining the wavelength or frequency of a wave, calculating the speed of a wave given its wavelength and frequency, or calculating the energy or intensity of a wave.
In summary, the electromagnetic wave equations, derived from Maxwell's equations, describe the behaviour of electric and magnetic fields and their propagation through space. These equations enable calculations related to wave properties such as wavelength, frequency, speed, amplitude, and intensity. Understanding and applying these equations are fundamental in studying and analysing electromagnetic waves and their numerous applications in fields such as communications, optics, and electronics.