Download Maxwell's Equations and the Principles of Electromagnetism by Richard Fitzpatrick PDF
By Richard Fitzpatrick
Designed for top department electromagnetism classes or as a reference for electric engineers and scientists, this e-book introduces Maxwell s equations and electromagnetic waves once attainable (i.e., within the first 3rd of the book), after which discusses electrostatics, magnetostatics, induction, etc., within the mild of these equations. The e-book additionally offers an intensive remedy of vector box idea which emphasizes the rotational invariance of the dot and go items, including div, grad, and curl, and hence provides a transparent actual motivation for using these constructs to explain electrical and magnetic fields. in contrast to many competing books, Maxwell s Equations & the rules of Electromagnetism covers issues similar to complicated potentials, retarded fields, forces on dielectric drinks, antenna thought, and Faraday rotation. *BRIEF desk OF CONTENTS: 1. advent. 2. Vectors and Vector Fields. three. Time-Independent Maxwell s Equations. four. Time-Dependent Maxwell s Equations. five. Electrostatic Calculations. 6. Dielectric and Magnetic Media. 7. Magnetic Induction.8.Electromagnetic strength and Momentum. nine. Electromagnetic Radiation. 10. Relativity and Electromagnetism. Appendixes. Index.
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Extra info for Maxwell's Equations and the Principles of Electromagnetism
Example text
Hence, Ar = A · er , etc. The volume element in this coordinate system is d3 r = r dr dθ dz. 164) respectively. Here, V(r) is a general vector field, and A (r) a general scalar field. Finally, the Laplacian is written ∇2 V = 1 ∂ r ∂r r ∂V ∂r + 1 ∂2 V ∂2 V + . 165) In the spherical polar coordinate system the Cartesian coordinates x, y, and z are replaced by r = x2 + y2 + z2 , θ = cos−1 (z/r), and φ = tan−1 (y/x). 26. Note that r and θ in the spherical polar system are not the same as their counterparts in the cylindrical system.
In vector notation. 6726 × 10−11 N m2 kg−2 . 4) Note that Coulomb’s law has the same mathematical form as Newton’s law of gravity. , | f2 | ∝ 1 . 5) However, these laws differ in two crucial respects. Firstly, the force due to gravity is always attractive (there is no such thing as a negative mass). Secondly, the magnitudes of the two forces are vastly different. Consider the ratio of the electrical and gravitational forces acting on two particles. This ratio is a constant, independent of the relative positions of the particles, and is given by |felectrical | |fgravitational | = |q1 | |q2 | 1 .
This tells us that the summation is equivalent to ∇ · A dV over the whole volume. Thus, the integral of A · dS over the outer surface is equal to the integral of ∇ · A over the whole volume, which proves the divergence theorem. 126) for any closed surface S. 21. (Note that the direction of the surface elements on S1 has been reversed relative to those on the closed surface. 21: Two surfaces spanning the same rim (right), and the equivalent closed surface (left). ) Thus, if ∇ · A = 0 then the surface integral depends on the rim but not the nature of the surface which spans it.