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Do Maxwell equations explain electrostatic and magnetostatic interactions? If they don't, what does? Is it compatible with Maxwell equations?
There are some materials for which we just can't - there isn't a simple scalar relating E and D fields OR the B and H fields.
Quote from: hamdani yusuf on 03/06/2023 06:59:04Do Maxwell equations explain electrostatic and magnetostatic interactions? If they don't, what does? Is it compatible with Maxwell equations? No, they are derived from experiments that show that a moving charge creates a magnetic field and a varying magnetic field induces a voltage in a conductor. These are essentially dynamic phenomena.
Hamdani, the biot-savart equation is the counterpart to coulomb, describing the magnetostatic.
Can it describe interaction between two permanent magnets?How about a magnet and a small ferromagnetic material?
To be honest I'm surprised Alancalverd uses a 1/r2 law as an approximation at any range
As outlined by @alancalverd , dipoles don't follow an inverse square law for the field strength they produce. At large enough distances, it's an inverse cube law. (To be honest I'm surprised Alancalverd uses a 1/r2 law as an approximation at any range - but very close it isn't a perfect 1/r3 law, which we both agree on)
The net force acting between the dipole and point entity X will be: FD = k X x / (R-δ /2)2 - k X x / (R+δ /2)2we can rewrite the above in the form: FD = [kXx/R2] / (1-δ /2R)2 - [kXx/R2] / (1+δ /2R)2For the condition δ <<2R, which was set as one of our assumptions, we are justified to apply the binomial approximation (1+x)n≈ 1+nx, or 1/(1+x)n ≈ 1-nx, valid for x<< 1. This reduces: 1/(1-δ /2R)2 to 1+δ /R, and 1/(1+δ /2R)2 to 1-δ /R The force field equation can therefore be approximated as: FD ≈ [kXx/R2](1+δ /R) - [kXx/R2](1-δ /R) FD ≈ [kXx/R2](1+δ /R - 1 + δ /R) FD ≈ 2kXxδ /R3 or simply FD ~ 1/R3 https://www.gsjournal.net/h/papers_download.php?id=1833
I'm sure you could calculate the precise acceleration of a flat-screen television in a 3T field,
So it experiences a force that depends on the gradient of the B field instead of being directly proportional to B
Classical theories don't tell where the quantization of energy comes from.
https://en.wikipedia.org/wiki/Planck_postulateThe Planck postulate (or Planck's postulate), one of the fundamental principles of quantum mechanics, is the postulate that the energy of oscillators in a black body is quantized, and is given byE = n h νwhere n is an integer (1, 2, 3, ...), h is Planck's constant, and ν (the Greek letter nu, not the Latin letter v) is the frequency of the oscillator.The postulate was introduced by Max Planck in his derivation of his law of black body radiation in 1900. This assumption allowed Planck to derive a formula for the entire spectrum of the radiation emitted by a black body. Planck was unable to justify this assumption based on classical physics; he considered quantization as being purely a mathematical trick, rather than (as is now known) a fundamental change in the understanding of the world.[1] In other words, Planck then contemplated virtual oscillators.In 1905, Albert Einstein adapted the Planck postulate to explain the photoelectric effect, but Einstein proposed that the energy of photons themselves was quantized (with photon energy given by the Planck?Einstein relation), and that quantization was not merely a feature of microscopic oscillators. Planck's postulate was further applied to understanding the Compton effect, and was applied by Niels Bohr to explain the emission spectrum of the hydrogen atom and derive the correct value of the Rydberg constant.
Planck's energy equation E = n.h.f
I think this is more intuitive,
Quote from: hamdani yusuf on 07/06/2023 08:32:29I think this is more intuitive, Nobody else seems to.
I think this is more intuitive, for following reason. Suppose we have a radiation source so dim that n=1 and f=1 Hz. Minimum value for E=h Joule. But radiation power is still undetermined. If it's radiated in 1 second then the power is h Watt. If it's radiated in 1000 second, then the power is h milliWatt.
In currently more common used form of equation, radiation power is not quantized,
Power isn't even a conserved quantity.
When power changes, where does the difference go?
There's no adequate justification to extrapolate it to other type of power or energy, such as gravitational potential energy.