By Richard Becker
Volume I, on electromagnetic idea, contains an creation to vector and tensor calculus, the electrostatic box, electrical present and the sector, and the idea of relativity. the second one quantity contains a self-contained creation to quantum concept that covers the classical rules of electron thought and quantum mechanics, difficulties related to one and several other electrons, radiation conception, and the relativistic conception of the electron. according to study by way of the good Harvard technological know-how historian Gerald Holton, this booklet essentially explains Maxwell's and Dirac's box equations and includes a profound dialogue and stylish use of the Helmholtz theorem on vector fields. issues of strategies look in the course of the textual content, that's illuminated via 148 illustrations.
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Extra info for Electromagnetic Fields and Interactions
6) the relation which remains correct even when some of the prisms considered cut out of S four, six, or even more surface elements. The volume element is designated for brevity here by dυ. 5) we immediately have as the component form of div u the expression independent of any relationship to the surface S. 5), the divergence of the field u is a scalar quantity independent of any coordinate system. 5) without the necessity of going by way of the component representation. For this the volume V is broken up into small volumes υ1, υ2,… so that, for each of these volumes υj, with surface Sj, the formula valid in the limit υj → 0, is written down, and this is summed over the volume.
The vector C, so defined, is called the vector product of A and B and is set equal to the above-defined outer product From this definition it follows that since Cz = Ccos〈 C,z〉, the z-component of A × B is to be understood to be the projection of the parallelogram area S ≡ C on the xy-plane. Moreover, the sum of two outer products represents a directed quantity whose z-component is equal to the sum of the projections of the two parallelogram areas on the xy-plane. Further, from the definition of the vector product there follows the invalidity of the commutative law.
On the left side all contributions corresponding to a surface element shared by two neighbouring volume elements cancel, for the simple reason that they always occur twice but with mutually opposite sign. 10) over the whole surface S remains. We summarize the foregoing results of this section as follows: for continuously distributed sources the total flux of a vector field u over a closed surface can be calculated by Gauss’s theorem as the volume integral of the divergence of u. The latter is therefore the proper measure of the strength or productiveness of the u-field.