Physics 1602 5 The Geometry of Electrostatic Fields
- 5.1 Gauss’ law
- 5.1.1 Flow, current density, and flux
- 5.1.2 Electric flux
- 5.1.3 Integral form of Gauss’ law
- 5.1.4 Charge density and point charges
- 5.2 Application of Gauss’ law to symmetric charge distributions
- 5.2.1 Spherical symmetries
- 5.2.2 Infinite cylindrical symmetries
- 5.2.3 Planar symmetries
- 5.3 Divergence
- 5.4 Gauss’ law in differential form
- 5.5 Calculating the electric potential from the electric field
- 5.5.1 Electric potential for the charged balloon
- 5.5.2 Electric potential for the infinite charged cylinder
- 5.5.3 Electric potential for planar problems
- 5.6 Physics of a surface charge layer
- 5.7 Potential energy (reprise)
- 5.8 Curl
- 5.8.1 Stokes’ theorem
- 5.8.2 Curl of electrostatic field
- 5.9 Poisson equation
- 5.10 Gaussian units (reprise)
6 Electrostatic fields and conductors 6.1 Ideal conductors 6.1.1 Planar conductor in the presence of planar external charge distribution 6.2 Charges and Cavities in conductors 6.2.1 Conductors as electrostatic shields 6.3 Planar conductors: image charge method 6.4 Capacitance and Capacitors 6.4.1 Energy in capacitors
7 Flowing charge 7.1 Current density 7.2 Charge conservation 7.2.1 The continuity equation 7.3 Microscopic Ohm’s law 7.3.1 Time-dependent screening of electric fields in a conductor 7.4 Conduction in “wires” 7.5 Current flow and Emf 7.5.1 Circuits 7.5.2 Power dissipation in conductors 7.5.3 Pairs of conductors having different conductivity 7.5.4 Parallel conductors 7.6 DC circuits 7.7 RC circuits 7.8 Microscopic physics of Ohm’s law 7.8.1 Thermodynamic distribution function
8 Electrostatic interactions and Special Relativity 8.1 Transformation of fields between inertial frames 8.1.1 Transformation of partial derivatives 8.2 Transformation of charge and current densities 8.3 Transformation of the electrostatic field 8.4 Gauss’ law 8.5 Transformation of electric potential 8.5.1 The vector potential for straight-line currents 8.6 Incompleteness of electrostatics
9 Magnetostatics 9.1 Lack of magnetic charges 9.2 Magnetic field from the vector potential 9.3 Magnetic forces and dimensions of magnetic field 9.4 Magnetic fields by direct integration 9.4.1 Circular current loop 9.4.2 Infinite line of current 9.4.3 Superposition of lines of current 9.4.4 Biot-Savart law 9.5 Ampere’s law 9.5.1 Magnetic field of finite radius cylinder of current 9.5.2 Magnetic field of the infinite sheet of current 9.6 Magnetic field generated by current loops 9.6.1 Single current loop, magnetic dipole 9.6.2 Multiple current loops 9.6.3 Magnetic field of a solenoid 9.7 Magnetic fields in Gaussian units 9.8 Magnetic forces 9.8.1 Motion of charged particle in a magnetic field 9.8.2 Forces on current-carrying wires
10 Induction 10.1 Lorentz transformation of electric and magnetic fields 10.1.1 Transformation #1 10.1.2 Transformation #2 10.1.3 Combining the results of LT #1 and LT #2 10.2 Magnetic induction 10.2.1 Conducting bar in a uniform field 10.2.2 Conducting bar in a non-uniform magnetic field 10.2.3 Conducting loop in a non-uniform magnetic field 10.2.4 Examples of magnetic induction 10.3 Time-dependent magnetic fields and electric induction 10.3.1 Conducting loop in non-uniform magnetic field, loop frame 10.3.2 Electric EMF and Faraday’s law 10.3.3 Examples of electric induction 10.3.4 Mutual inductance 10.4 Self-inductance 10.4.1 Energy stored in an “inductor”