A Student's Guide to Maxwell's EquationsGauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere–Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter. |
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Ampere Ampere–Maxwell law Ampere’s law Amperian loop bound charge capacitor changing magnetic field charge density closed surface component curl current density cylinder d~l ¼ defined definition dielectric differential form direction displacement current distance divergence theorem dot product electric charge electric current electric field lines electric flux enclosed charge enclosed current Example Faraday’s law field field points find the electric first fluid flux form of Faraday’s form of Gauss’s free space Gauss’s law gradient here’s induced electric field integral form law for electric law for magnetic left side line integral magnetic field lines magnitude Maxwell Maxwell’s Equations nda¼ negative charge path permeability permittivity of free perpendicular plates positive charge problems radius rate of change right side right-hand rule scalar field segment shown in Figure solenoid special Gaussian surface specified sphere spherical straight wire surface integral surface normal understand unit normal vector field volume zero
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Seite 81 - C (left-hand side) is equal to the negative of the time rate of change of the magnetic flux through the surface S (righthand side).
Seite 88 - Li (5.36) where N is the number of turns, A is the cross-sectional area and B is the magnetic flux density.
Seite 131 - Electricity and Magnetism, Berkeley Physics Course, Vol. 2, McGraw-Hill, New York, 1965, pp. 147-181. 2. t. Page, "The Emission Theory of Electromagnetism,
Seite 45 - Work. the horizontal plane is x and the component of the force in the direction of the displacement is F cos d.
Seite 81 - T=mBs'my (5) where y is the angle between the normal to the plane of the loop and the direction of B (see Fig.
Seite 77 - The direction of the magnetic field is given by the "right-hand rule": If you curl the fingers of your right hand in the direction of current flow, the thumb points in the direction of the axial (BJ field vector.
Seite 29 - An important relationship exists between the integral of the normal component of the electric field over a closed surface and the total charge enclosed by the surface. This relationship, known as Gauss' law, will now be investigated in more detail.
Seite i - He is a member of the American Physical Society (APS), the American Association of Physics Teachers (AAPT), and the Institute of Electrical and Electronics Engineers (IEEE).
Seite 22 - Similarly, we can show that the electric field at a distance r from a point charge in a uniform dielectric, (4.2.5), and the Coulomb force, (4.2.6), are each diminished by the factor e.
