Maxwell's equations are a set of four equations that describe the behaviour of electric and magnetic fields and their interactions with matter. They were first published in 1865 by James Clerk Maxwell and form the basis of classical electromagnetism. The equations relate the sources of the fields (charges and currents) to the fields themselves and describe how they propagate through space and change with time. These equations have far-reaching consequences, including the prediction of electromagnetic waves (such as light) and the unification of electricity and magnetism into a single theory. Maxwell's equations in free space are the four equations that describe the behavior of electric and magnetic fields in the absence of charges and currents. These equations are: Gauss's law for electric fields: The total electric flux through any closed surface is proportional to the charge enclosed within that surface. Gauss's law for magnetic fields: There are no magnetic monopoles, so the total magnetic flux through a closed surface is always zero. Faraday's law of induction: A changing magnetic field generates an electric field. Ampere's law with Maxwell's correction: The circulation of the magnetic field around a closed loop is proportional to the current flowing through the loop, plus a term that accounts for the change in the electric field over time. These equations are valid in the absence of charges and currents and in a static (time-invariant) electromagnetic field. They can be used to analyze the behavior of electromagnetic fields in a wide range of situations, from simple circuits to more complex systems. The solutions to these equations also provide insight into the nature of electromagnetic waves, which are fundamental to the study of optics, radio, and other areas of physics.

1. MAXWELL’S EQUATIONS
IN FREE SPACE AND CONDUCTING MEDIA

2. Maxwell’s equations
In free space
and Conducting
media

3. James Clark
Maxwell
Maxwell’s Equations :
First equation : Is a form of “Gauss’s law”.
Electric field
Second equation : It is also form of “Gauss’s law”.
Magnetic field
Third equation : Is a form of “Faradays’s law”.
Fourth equation : Is a form of “Ampere’s law”.

4. Maxwell’s equations integral form explain how the electric charges and electric currents produce
magnetic and electric fields. Maxwell’s equations (there are 4) provide a mathematical description
at the macroscopic level (not the quantum mechanical level) for electromagnetism.
The four laws:
1. Gauss’s law: It states that the net quantity of the electric flux leaving a
sample volume is proportional to the charge inside the volume.
2. Gauss’s Law for Magnetism: It states that the impossibility of creating a
magnetic monopole; the total magnetic flux through a closed surface is zero.
3. Maxwell-Faraday Equation: The voltage induced in a closed loop is
proportional to the rate of change of the magnetic flux that the loop encloses
4. Ampere-Maxwell Circuital Law: The magnetic field induced around a
closed loop is proportional to the electric current plus displacement current
(rate of change of electric field) that the loop encloses.
IMPORTANCE OF MAXWELL’s EQUATIONS

5. Maxwell’s equations in free space
Volume charge
density
free current
density
In free space
= 0
and
j = 0
Conductivity,
= 0
J = . E = 0

6. DIFFERENTIAL FORM:

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INTEGRAL FORM:

8. THANK YOU