del
What it is
Del is a three dimensional per unit distance differential operator. It has
dimensions of the reciprocal of distance. It is a measure of the rate of
increase of the wave function. It is associated with del^2, the Laplace Operator
which is a three dimensional property which has dimensions of per unit area.
History
William Hamilton (1805-1865), Marquis Laplace (1749-1827) and James Clerk
Maxwell (1831-1879) developed and applied concepts involving the del factor to
the solution of physical problems.
Maxwell used the concept of "del" in formulating his four equations
which basically state:
1. An electric field arises from electric charge. (An expression of Coulomb's
Law.)
del . D = charge density
2. There are no isolated magnetic poles.
del . B = 0
3. Electric fields are produced by changing magnetic fields. (Faraday's Law
of induction.)
del x E = B / time
4. Circulating magnetic fields are produced by changing electric fields and
by electric currents.
(Maxwell's extension of Ampere's law to include changing fields.)
del x H = J + j*2 pi* D
Common equations
del = i d / dx
del . B = 0
del . D = charge density
del x E = B / time
del x H = J + j*2 pi* D
Units
reciprocal distance
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