9 Circuits
9.1 Current and voltage................ 530
Current, 530.—Circuits, 533.—Voltage, 534.—Resistance, 539.—
Current-conducting properties of materials, 548.
9.2 Parallel and series circuits............. 552
Schematics, 552.—Parallel resistances and the junction rule, 553.—
Series resistances, 557.
Problems...................... 564
Exercises...................... 57210 Fields
10.1 Fields of force.................. 577
Why fields?, 577.—The gravitational field, 579.—The electric field,
583.
10.2 Potential related to field.............. 590
One dimension, 590.—Two or three dimensions, 593.
10.3 Fields by superposition.............. 595
Electric field of a continuous charge distribution, 595.—The field
near a charged surface, 601.
10.4 Energy in fields................. 604
Electric field energy, 604.—Gravitational field energy, 609.—Magnetic
field energy, 609.
10.5 LRC circuits................... 611
Capacitance and inductance, 611.—Oscillations, 615.—Voltage and
current, 617.—Decay, 622.—Review of complex numbers, 625.—
Euler’s formula, 627.—Impedance, 628.—Power, 632.—Impedance
matching, 635.—Impedances in series and parallel, 637.
10.6 Fields by Gauss’ law............... 639
Gauss’ law, 639.—Additivity of flux, 643.—Zero flux from outside
charges, 643.—Proof of Gauss’ theorem, 647.—Gauss’ law as a
fundamental law of physics, 647.—Applications, 648.
10.7 Gauss’ law in differential form........... 651
Gauss’s law as a local law, 651.—Poisson’s equation and Laplace’s
equation, 655.—The method of images, 655.
Problems...................... 657
Exercises...................... 66911 Electromagnetism
11.1 More about the magnetic field........... 673
Magnetic forces, 673.—The magnetic field, 677.—Some applica-
tions, 681.—No magnetic monopoles, 683.—Symmetry and hand-
edness, 685.
11.2 Magnetic fields by superposition.......... 687
Superposition of straight wires, 687.—Energy in the magnetic field,
691.—Superposition of dipoles, 691.—The g factor (optional), 695.—
The Biot-Savart law (optional), 696.
11.3 Magnetic fields by Ampere’s law.......... 700`
Amp`ere’s law, 700.—A quick and dirty proof, 702.—Maxwell’s
equations for static fields, 703.10 Contents