Maxwell Equation
The Maxwell equations
Introduction:-
One of Newton's great achievements was to show that all of the phenomena of classical mechanics can be deduced as consequences of three basic, fundamental laws, namely Newton's laws of motion. It was likewise one of Maxwell's great achievements to show that all of the phenomena of classical electricity and magnetism – all of the phenomena discovered by Oersted, Ampère, Henry,
Faraday and others whose names are commemorated in several electrical units – can be deduced as consequences of four basic, fundamental equations. We describe these four equations in this chapter, and, in passing, we also mention Poisson's and Laplace's equations. We also show how
Maxwell's equations predict the existence of electromagnetic waves that travel at a speed of 3 % 108 m s−1. This is the speed at which light is measured to move, and one of the most important bases of our belief that light is an electromagnetic wave.
Before embarking upon this, we may need a reminder of two mathematical theorems, as well as a reminder of the differential equation that describes wave motion.
The two mathematical theorems that we need to remind ourselves of are:
The surface integral of a vector field over a closed surface is equal to the volume integral of its divergence. The line integral of a vector field around a closed plane curve is equal to the surface integral of its curl.
There are four basic equations, called Maxwell equations, which form the axioms of electrodynamics. The so called local forms of these equations are the following:
rot H = j + D/t (1) rot E = - B/t (2) div B = 0 (3) div D = (4)
Here rot (or curl in English literature) is the so called vortex density, H is vector of the magnetic field strength, j is the current density vector, D/t is the time derivative of the electric displacement vector D, E is the electric field strength, B/t is the time derivative of the magnetic induction vector B,
Introduction:-
One of Newton's great achievements was to show that all of the phenomena of classical mechanics can be deduced as consequences of three basic, fundamental laws, namely Newton's laws of motion. It was likewise one of Maxwell's great achievements to show that all of the phenomena of classical electricity and magnetism – all of the phenomena discovered by Oersted, Ampère, Henry,
Faraday and others whose names are commemorated in several electrical units – can be deduced as consequences of four basic, fundamental equations. We describe these four equations in this chapter, and, in passing, we also mention Poisson's and Laplace's equations. We also show how
Maxwell's equations predict the existence of electromagnetic waves that travel at a speed of 3 % 108 m s−1. This is the speed at which light is measured to move, and one of the most important bases of our belief that light is an electromagnetic wave.
Before embarking upon this, we may need a reminder of two mathematical theorems, as well as a reminder of the differential equation that describes wave motion.
The two mathematical theorems that we need to remind ourselves of are:
The surface integral of a vector field over a closed surface is equal to the volume integral of its divergence. The line integral of a vector field around a closed plane curve is equal to the surface integral of its curl.
There are four basic equations, called Maxwell equations, which form the axioms of electrodynamics. The so called local forms of these equations are the following:
rot H = j + D/t (1) rot E = - B/t (2) div B = 0 (3) div D = (4)
Here rot (or curl in English literature) is the so called vortex density, H is vector of the magnetic field strength, j is the current density vector, D/t is the time derivative of the electric displacement vector D, E is the electric field strength, B/t is the time derivative of the magnetic induction vector B,