Archive for the ‘Physics’ Category

Maxwell’s Equations

February 6, 2013

The differential form….

\nabla\times{\bf E}=-\displaystyle\frac{\partial{\bf B}}{\partial t}
\nabla\times{\bf B}=\mu_0{\bf J}+\displaystyle\frac{1}{c^2}\frac{\partial{\bf E}}{\partial t}
\nabla\cdot{\bf E} = \displaystyle\frac{\rho}{\epsilon_0}
\nabla\cdot{\bf B} = 0

These are my “favorite” equations. These equations serve as the cornerstone of all of electrical engineering. The result of the work of many people over very many years and published in their modern form by James Clerk Maxwell (1831-1879), these equations played a crucial role in the history of physics. Strictly speaking it may be said that Maxwell’s Equations are “wrong” and have been replaced by the laws of quantum electrodynamics which give an even more fundamental description of the basic interaction of electrical forces with matter. Even so, Maxwell’s Equations are used to describe all classical electrical phenomena commonly appearing in engineering. In the form appearing above the equations are called the vacuum Maxwell Equations which means that all charge in a system is treated as free charge. This formulation is particularly useful in Plasma Physics.