Electromagnetism (calculus based):

Electrostatics: electric charge, point charge. The atomic nature of matter: electron, proton, neutron, elementary charge, quarks. Coulomb's law. Benjamin Franklin: sign convention, tribolelectric series, the conservation of electric charge. Polarization vs. influence.

Electric field: vector field. Electric field lines, electric flux, flux density. The superposition principle of electric fields. The concept of test charge. Electric dipole, dipole moment, dipole field. Gauss's law: sources and sinks of the electric field. Volumetric charge density, surface charge density, linear charge density, and the electric field produced by these electric charge distributions. Integral and differential form of Gauss's law: the third Maxwell equation. Electric field and displacement field.

Electric potential: scalar field. Potential energy, potential, potential difference, voltage. Electric field as the negative gradient of the potential: steepest descent. Potential as the negative line integral of the electric field. Conductors in electrostatics, equipotential surfaces.

Capacitors: applications. Parallel plate capacitor, capacitance. Storing charge and energy. Energy density of the electric field. Dielectrics: dielectric constant or relative permittivity. The relation between electric field, polarization and displacement. Capacitors in parallel and in series: equivalent capacitance.

Electric current: the flow of electric charge. Current density. Drift velocity. Ohm's law: macroscopic and microscopic. Resistance, resistivity, conductance, conductivity and their units. Power dissipated by a resistor, Joule heat.

DC circuits: batteries and resistors. EMF: electromotive force, terminal voltage, internal resistance. Electric circuits: voltage and current. Kirchhoff's rules: 1st: junction rule (conservation of electric charge), 2nd: loop rule (conservation of energy). Resistors in series and in parallel: equivalent resistance. Delta-Y transformation, Wheatstone bridge. Galvanometer, voltmeter, ampermeter or ammeter. Double-loop circuits. RC-circuits.

Magnetic fields and magnetism: point charge in magnetic field: Lorentz force. Vector product, right hand rule. Cyclotron, CRT, mass spectrometer, isotope separator, velocity selector. Hall effect. Force on a current carrying wire. Magnetic dipole moment, torque on a magnetic dipole, potential energy of a magnetic dipole inside a magnetic field. Magnetic field pruduced by a current carrying wire: Oersted experiment. Ampere's law, Biot-Savart law: the 2nd Maxwell equation. The B-field is source- and sink-free: the 4th Maxwell eq. Straight wire: infinite and finite, cicular loop, solenoid, toroid. Force between two current carrying wire: the metric definition of ampere. Magnetism of matter: paramagnetism, diamagnetism and ferromagnetism. Magnetic data storage: tapes and disks.

Electromagnetic induction: magnetic flux, Faraday's law of induction, Lenz's law: the 1st Maxwell equation. Motional and rotational EMF. The generation of electric power. Eddy currents. Self-induction. Magnetic flux-linkage. Mutual vs. self-induction. Solenoid: B-field, flux, flux linkage, energy. Energy density of the magnetic field. RL-circuits.

AC circuits: alternating voltage and current. RMS: the effective value. Resistor, inductor, capacitor, AC generator: driven RLC circuit. Resistance, capacitive and inductive reactance, impedance. The concept of phasor. Current resonance in RLC circuit. LC-circuit, Thomson formula. Damped oscillations. Power in AC circuits: apparent, true and reactive power. Phase angle, power factor. Transmitting AC power, transformer. Edison and Tesla, the war of currents.

Electromagnetic waves. Experiments: Hertz, Marconi, Braun, Tesla. The missing piece: displacement current. The wave equation: the speed of the light. The metric definition of meter. The electromagnetic spectrum: long, medium and short waves, microwaves, infrared (IR), visible, ultraviolet (UV), x-ray, gamma ray. Momentum and energy carried by electromagnetic waves: radiation pressure, intensity. Poynting vector. The solar constant. Polarization of EM waves. Intensity: one half rule and Malus's law. Application: LCD displays. Optical acivity. Pasteur.

Geometric optics: reflection and refraction, Snell's law. Index of refraction, chromatic dispersion. Polarization by reflection, Brewster's angle. Total internal reflection, optical fibers. Fermat's Principle: the principle of shortest time. Mirrors and lenses, focal lengths. Mirror and lens equation. Real and virtual images. Lateral magnification. Lensmaker's equation. Optical instruments: eye, camera, projector, microscope, telescopes, magnifying glass. Far and near sighted eye: glasses, diopter.

Wave optics: Huygens, Young, Fresnel, Fraunhofer. Huygens principle. Phase, phase angle. Interference: constructive and destructive. Diffraction, diffraction grating. Single slit diffraction. Double slit. Thin film interference: reflection and transmission. Phase jump in reflection. Rayleigh's criterion for circular apertures.

Special relativity: observation and experiments: stellar aberration, Bradley; Fizeau's experiment; Michelson-Morley experiment. Einstein's theory of relativity. The two postulates: 1st: the invariance of physical laws, 2nd: the constancy of the speed of the light. Space and time: space-time. Proper time, time dilatation. Proper length, Lorentz contraction. Space-time interval, Minkowski space. Twin paradox. Doppler effect. Red-shift of star light. The expansion of the Universe. Relativistic energy, rest energy, rest mass. Relativistic momentum.