## Learning objectives

## After completing the topic, the student will be able to:

- Explore the Maxwell's four basic equations of electromagnetism and their implications that lead to the birth of classical electrodynamics.
- Understand how electromagnetic waves can be transmitted from one place to another place with out the means of any physical contact.
- Discuss and determine the energy carried by the electromagnetic waves and its relevant applications in everyday science scenarios.
- Calculate the momentum and pressure exerted by an electromagnetic wave so as to discover the range of the electromagnetic wave.
- Discover various regions of electromagnetic spectrum based on their frequency and wavelength and also identify different types of regions as we move above the earth's surface.

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We know that electric current produces a magnetic field. We also know that when a conducting loop is moved through a magnetic field, we have electric current induced in the loop. Thus time varying electric and magnetic fields produce each other. This symmetry is very interesting and is one of the most fundamental observations in physics.

James Clark Maxwell (1831 – 1879) formulated a set of equations to explain these effects. There are four equations known as Maxwell′s equations that deal with electric and magnetic fields and their sources (charge and current densities). Together with the Lorentz force equation, the Maxwell′s equations give mathematically all the basic laws of electromagnetism.

The most important outcome of Maxwell′s equation is the presence of electromagnetic wave. Electromagnetic wave propagates in medium when there is a time varying electric and magnetic field present and the speed of propagation is close to the speed of light.

Far reaching conclusion was drawn from this observation – that light itself is an electromagnetic wave. At the heart of production of electromagnetic waves is an oscillating electric charge. These oscillating charges produce an oscillating magnetic field (or flux) and an oscillating magnetic field, in turn, produces an oscillating electric field!

**Charge density (ρ)**

Charge density is a measure of electric charge per unit volume of space, in one, two or three dimensions. The linear, surface, or volume charge density is the amount of electric charge per unit length, surface area, or volume.

**Current density (J)**

Current density is a measure of the density of flow of a conservedcharge, in other words flux of the charge.

**Electric displacement field (D)**

In a dielectric material the presence of an electric field **E** causes the bound charges in the material to slightly separate, inducing a local electric dipole moment. The electric displacement field **D** is defined as

**D = ε _{0} E + P**

where ε

_{0}is the permittivity of free space, and

**P**is the (macroscopic) density of the permanent and induced electric dipole moments in the material, called the polarization density. Separating the total volume charge density into free and bound charges.