Search results
Results from the WOW.Com Content Network
The above equations are the microscopic version of Maxwell's equations, expressing the electric and the magnetic fields in terms of the (possibly atomic-level) charges and currents present. This is sometimes called the "general" form, but the macroscopic version below is equally general, the difference being one of bookkeeping.
[24] [25] Maxwell deals with the motion-related aspect of electromagnetic induction, v × B, in equation (77), which is the same as equation (D) in Maxwell's original equations as listed below. It is expressed today as the force law equation, F = q ( E + v × B ) , which sits adjacent to Maxwell's equations and bears the name Lorentz force ...
Oliver Heaviside reduced the complexity of Maxwell's theory down to four partial differential equations, [118] known now collectively as Maxwell's Laws or Maxwell's equations. Although potentials became much less popular in the nineteenth century, [119] the use of scalar and vector potentials is now standard in the solution of Maxwell's ...
Maxwell's relations are a set of equations in thermodynamics which are derivable from the symmetry of second derivatives and from the definitions of the thermodynamic potentials. These relations are named for the nineteenth-century physicist James Clerk Maxwell .
Eighteen of Maxwell's twenty original equations can be vectorized into six equations, labeled to below, each of which represents a group of three original equations in component form. The 19th and 20th of Maxwell's component equations appear as and below, making a total of eight vector equations. These are listed below in Maxwell's original ...
The four modern Maxwell's equations, as laid down in a publication by Oliver Heaviside in 1884, had all appeared in Maxwell's 1861 paper. Heaviside however presented these equations in modern vector format using the nabla operator (∇) devised by William Rowan Hamilton in 1837, Of Maxwell's work, Albert Einstein wrote: [4]
Using the Maxwell equations, one can see that the electromagnetic stress–energy tensor (defined above) satisfies the following differential equation, relating it to the electromagnetic tensor and the current four-vector , + = or , + =, which expresses the conservation of linear momentum and energy by electromagnetic interactions.
Because of the linearity of Maxwell's equations in a vacuum, solutions can be decomposed into a superposition of sinusoids. This is the basis for the Fourier transform method for the solution of differential equations. The sinusoidal solution to the electromagnetic wave equation takes the form