## Introduction to electrodynamicsFeatures a clear, accessible treatment of the fundamentals of electromagnetic theory. Its lean and focused approach employs numerous examples and problems. Carefully discusses subtle or difficult points. Contains numerous, relevant problems within the book in addition to end of each chapter problems and answers. |

### From inside the book

Results 1-3 of 36

Page 37

These corollaries are analogous to those for the gradient theorem. We shall

develop the parallel further in due course. Example 8 Suppose v = (2x2 + 3y2)j +

(4yz2)k. Let's check Stokes' theorem for the square surface shown in Fig. 1.34.

Here V X v = (4z2 - 2x)i + 2z& and da = dy dz i (In saying that da points in the x

direction, we are committing ourselves to a counterclockwise line integral. We

could as well

Since x = 0 ...

These corollaries are analogous to those for the gradient theorem. We shall

develop the parallel further in due course. Example 8 Suppose v = (2x2 + 3y2)j +

(4yz2)k. Let's check Stokes' theorem for the square surface shown in Fig. 1.34.

Here V X v = (4z2 - 2x)i + 2z& and da = dy dz i (In saying that da points in the x

direction, we are committing ourselves to a counterclockwise line integral. We

could as well

**write**da = — dy dz i, but then we would be obliged to go clockwise.)Since x = 0 ...

Page 241

[This is tough, so I'll give you a start: 1 B, S-kR3 BdT

Problem 1.61(b). Now put in (5.57), and do the surface integral first, showing that

1 4 — da. = — xr *. 3 (see Fig. 5.58).] (b) Show that the average magnetic field

due to steady currents outside the sphere is the same as the field they produce at

the center. Problem 5.49 I worked out the multipole expansion for the vector

potential of a line current because that's the most common type, and in some

respects ...

[This is tough, so I'll give you a start: 1 B, S-kR3 BdT

**Write**B as (V X A), and applyProblem 1.61(b). Now put in (5.57), and do the surface integral first, showing that

1 4 — da. = — xr *. 3 (see Fig. 5.58).] (b) Show that the average magnetic field

due to steady currents outside the sphere is the same as the field they produce at

the center. Problem 5.49 I worked out the multipole expansion for the vector

potential of a line current because that's the most common type, and in some

respects ...

Page 316

... what this freedom entails. Suppose we have two sets of potentials, ( V, A) and (

V" , A ' ), which correspond to the same electric and magnetic fields. By how much

can they differ?

their curls must be equal (7.63), and hence V Xa = 0 We can therefore

the gradient of some scalar: a = VX The two potentials also give the same E, so (

7.64) requires that da or ...

... what this freedom entails. Suppose we have two sets of potentials, ( V, A) and (

V" , A ' ), which correspond to the same electric and magnetic fields. By how much

can they differ?

**Write**A' = A + a and V = V + /3 Since the two A's give the same B,their curls must be equal (7.63), and hence V Xa = 0 We can therefore

**write**a asthe gradient of some scalar: a = VX The two potentials also give the same E, so (

7.64) requires that da or ...

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#### LibraryThing Review

User Review - astropi - LibraryThingThis is one of my all-time favorite science books! Does a BRILLIANT job of presenting the physics, and reviews the basic math (divergence, Stoke's Theorem, etc). This book is a MUST for anyone in ... Read full review

### Contents

Vector Analysis | 6 |

Electrostatics | 61 |

Surface Charge | 103 |

Copyright | |

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### Common terms and phrases

Ampere's law angle answer assume atom axis Biot-Savart law bound charge boundary conditions calculate capacitor charge density charge distribution charge q clock components conductor configuration conservation constant coordinates Coulomb Coulomb's law curl current density cylinder derivative direction distance divergence theorem electric and magnetic electric field electrodynamics electromagnetic electron electrostatics energy Example field inside Figure Find the electric Find the potential flux formula free charge frequency function Gauss's law gradient infinite infinitesimal Laplace's equation linear dielectric Lorentz force law Lorentz transformation magnetic dipole magnetic field magnetic force magnetostatics Maxwell's equations momentum motion moving origin particle perpendicular plane point charge polarization Poynting vector Problem radiation region relativistic relativity scalar Section shown in Fig solenoid Solution sphere of radius spherical steady current Suppose surface charge tion total charge V X B V X E vector potential velocity volume wave zero