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Maxwell's equations: meaning, derivation and applicability - Classical Physics

Maxwell's equations: meaning, derivation and applicability - Classical Physics
Quote So if Coulombs law works best for you, then use coulomb's law - there's no need to re-invent the wheel. As far as the original problem goes it is solved, but it uncovered great many things for me, so what is left now is curiosity because this solution implies Coulomb's and Biot-Savart law tell different and more complete story than Maxwell's equations and yet they are supposed to talk about the same E and B fields. There are two kinds of fields, "radial" like gravity and electric fields, and we have "rotational", like vortexes, whirlpools or magnetic fields. Uniform and constant "radial" field potentials have zero divergence and zero rotation (curl), it's a uniform magnitude distribution and inverse square law which defines topology and geometry of an electric field, not the other way around. This page here shows you how to get coulomb's law from maxwell's first equation: -- This page says: -"Gauss's law can be derived from Coulomb's law Related:  physicsPhysics Course Materials

Free Physics Video and Audio Courses These are the free physics video and audio courses. They are ordered based on their difficulty, starting with easiest first and ending with the most difficult. Also if you love physics, check out my friend's video websites dedicated to three famous physicists: And here are the physics video lectures: Descriptive introduction to physics: No prior physics is required. Classical Mechanics: In addition to the basic concepts of Newtonian Mechanics, Fluid Mechanics, and Kinetic Gas Theory, a variety of interesting topics are covered in this course: Binary Stars, Neutron Stars, Black Holes, Resonance Phenomena, Musical Instruments, Stellar Collapse, Supernovae, Astronomical observations from very high flying balloons (lecture #35), and you will be allowed a peek into the intriguing Quantum World. Introductory Physics Introduction to forces, kinetics, equilibria, fluids, waves, and heat. Electricity and Magnetism: Vibrations and Waves: Symmetry, Structure, and Tensor Properties of Materials

Perspectives of Hans Bethe The Second Law and Energy (second law event) 10/05/2007 1:00 PM Broad InstituteSteven Chu, Secretary of EnergyDescription: This Nobel Prize"winning scientist admits to staying up late the night before his talk to bone up on thermodynamics. He puts his research to good use, discussing the history and application of the laws of thermodynamics, which have served as "the scientific foundation of how we harness energy, and the basis of the industrial revolution, the wealth of nations." Taking Watt's 1765 steam engine, Stephen Chu illustrates basic principles of thermodynamics -- that energy is conserved, that you can do work from heat, especially when you maximize the difference in temperature in the system and minimize heat dissipation from friction. Chu offers another form of the laws: You can't win; you can't break even; and you can't leave the game. The game hasn't changed all that much in the past few centuries. credit MIT World -- special events and lectures license MIT TechTV

Seminar: Visualizing Special Relativity The following text is that of a seminar presented to the ANU Physics Department on 25 September 1997. Note that the links to animations will not function. Animations may be downloaded elsewhere. Antony Searle Australian National University Distinguished Scholars Program Animations The Lorentz factor can be thought of as the degree of relativistic effects. An explanation of the Head-up Display: Aberration Animations: THE DOPPLER EFFECT Like sound, light undergoes frequency shifting when and observer moves at comparable speeds. where v is the velocity of the observer, a and n are the angle subtended and frequency of the photon in the rest frame, and n' is the frequency recorded by the moving observer The relativistic formula is similar, but corrected for time dilation Doppler Shift Animations: Headlight Effect Animations: Animations:

General relativity General relativity, or the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1916[1] and the current description of gravitation in modern physics. General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations. Some predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Einstein's theory has important astrophysical implications. History[edit] Albert Einstein developed the theories of special and general relativity.

QM Experiments for Undergraduates Textbook My book is titled Quantum Mechanics: Theory and Experiment, and is written for a junior/senior level quantum mechanics class. It is unique in that it describes not only quantum theory, but also presents laboratories that explore truly modern aspects of quantum mechanics. Description Technology has advanced to the point where truly modern experiments which explore the fundamentals of quantum mechanics are accessible to undergraduates. Overview · Slides of a talk given at Amherst College in Oct. 2004. · Slides of a talk given at AAPT Meeting, July 2006. · Slides of a talk given at AAPT Meeting, July 2006. Experiments Proof of the Existence of Photons (the Grangier Experiment) This experiment duplicates the experiment of Grangier, Roger and Aspect [1], in which they demonstrate that if a single photon is incident on a beamsplitter, it can only be detected at one of the outputs (not both.) [1] P. Single Photon Interference Bell Inequalities [2] D. [3] D. Hardy’s Test of Local Realism

Physics World reveals its top 10 breakthroughs for 2011 The two physics stories that dominated the news in 2011 were questions rather than solid scientific results, namely "Do neutrinos travel faster than light?" and "Has the Higgs boson been found?". However, there have also been some fantastic bona fide research discoveries over the last 12 months, which made it difficult to decide on the Physics World 2011 Breakthrough of the Year. But after much debate among the Physics World editorial team, this year's honour goes to Aephraim Steinberg and colleagues from the University of Toronto in Canada for their experimental work on the fundamentals of quantum mechanics. Using an emerging technique called "weak measurement", the team is the first to track the average paths of single photons passing through a Young's double-slit experiment – something that Steinberg says physicists had been "brainwashed" into thinking is impossible. We have also awarded nine runners-up (see below). 1st place: Shifting the morals of quantum measurement

Charges and Fields - Electric Charges, Electric Field, Electric Potential Topics Electric Field Electrostatics Equipotential Electrostatic Potential Electric Charges Voltage Description Arrange positive and negative charges in space and view the resulting electric field and electrostatic potential. Sample Learning Goals Determine the variables that affect the strength and direction of the electric field for a static arrangement of charges.Investigate the variables that affect the strength of the electrostatic potential (voltage).Explain equipotential lines and compare them to the electric field lines.For an arrangement of static charges, predict the electric field lines. Quantum Diaries (Thoughts on work and life from particle physicists from around the world.)

Physics Simulation with Java Gravitational lens A light source passes behind a gravitational lens (point mass placed in the center of the image). The aqua circle is the light source as it would be seen if there was no lens, white spots are the multiple images (or Einstein ring) of the source. A gravitational lens is a distribution of matter (such as a cluster of galaxies) between a distant light source and an observer, that is capable of bending the light from the source as the light travels towards the observer. This effect is known as gravitational lensing, and the amount of bending is one of the predictions of Albert Einstein's general theory of relativity.[1][2] (Classical physics also predicts the bending of light, but only half that predicted by general relativity.[3]) Although Einstein made unpublished calculations on the subject in 1912,[4] Orest Khvolson (1924)[5] and Frantisek Link (1936)[citation needed] are generally credited with being the first to discuss the effect in print. Description[edit] 1. 2. 3. History[edit] Notes

Problem of Reciprocity Back to main course page John D. Norton Department of History and Philosophy of Science University of Pittsburgh Background reading: J. Schwartz and M. McGuinness, Einstein for Beginners. What's the Problem? Relativity theory tells us that a moving clock is slowed down and a moving rod is shrunk in the direction of its motion. Each finds the other's clocks slowed and rods shrunk. The Car and the Garage That each finds the other's clocks slowed and rods shrunk is troubling. That perspectival effect should not worry anyone. Now image that we drive the car at 86.6% speed of light through the garage from right to left. Now this is a serious problem. More formally, we have a true paradox. It IS the case that car is fully trapped with in the garage. It is usually take to be a fatal problem when a theory is shown to harbor contradictions. Relativity of Simultaneity... ...Solves the Problem Here's an animated version of this process.

Gravitational microlensing Gravitational microlensing is an astronomical phenomenon due to the gravitational lens effect. It can be used to detect objects ranging from the mass of a planet to the mass of a star, regardless of the light they emit. Typically, astronomers can only detect bright objects that emit lots of light (stars) or large objects that block background light (clouds of gas and dust). These objects make up only a tiny fraction of the mass of a galaxy. Microlensing allows the study of objects that emit little or no light. When a distant star or quasar gets sufficiently aligned with a massive compact foreground object, the bending of light due to its gravitational field, as discussed by Einstein in 1915, leads to two distorted unresolved images resulting in an observable magnification. Since microlensing observations do not rely on radiation received from the lens object, this effect therefore allows astronomers to study massive objects no matter how faint. How it works[edit] History[edit] . . . . .

Math, Physics, and Engineering Applets Oscillations and Waves Acoustics Signal Processing Electricity and Magnetism: Statics Electrodynamics Quantum Mechanics Linear Algebra Vector Calculus Thermodynamics Miscellaneous Licensing info. Links to other educational sites with math/physics-related information or java applets useful for teaching: And when you get tired of learning, here is some fun stuff: Java Pong Applet a cute little pong game I wrote a while ago.