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# Maxwell's equations

| 🗖 nosplit | ↑ parent "Particle physics" | words: 408 | descendant words: 1k | descendants: 27
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Unified all previous electro-magnetism theories into one equation.
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Explains the propagation of light as a wave, and matches the previously known relationship between the speed of light and electromagnetic constants.
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The equations are a limit case of the more complete quantum electrodynamics, and unlike that more general theory account for the quantization of photon.
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The equations are a system of partial differential equation.
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The system consists of 6 unknown functions that map 4 variables: time t and the x, y and z positions in space, to a real number:
• , , : directions of the electric field
• , , : directions of the magnetic field
and two known input functions:
• : density of charges in space
• : current vector in space. This represents the strength of moving charges in space.
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Due to the conservation of charge however, those input functions have the following restriction: $$Equation 5. Charge conservation ∂t∂ρ​+∇⋅J=0 (5)$$
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Also consider the following cases:
• if a spherical charge is moving, then this of course means that is changing with time, and at the same time that a current exists
• in an ideal infinite cylindrical wire however, we can have constant in the wire, but there can still be a current because those charges are moving
Such infinite cylindrical wire is of course an ideal case, but one which is a good approximation to the huge number of electrons that travel in a actual wire.
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The goal of finding and is that those fields allow us to determine the force that gets applied to a charge via the Equation 10. "Lorentz force", and then to find the force we just need to integrate over the entire body.
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Finally, now that we have defined all terms involved in the Maxwell equations, let's see the equations:
🔗$$Equation 6. Gauss' law divE=ε0​ρ​ (6)$$
🔗$$Equation 7. Gauss's law for magnetism divB=0 (7)$$
🔗$$Equation 8. Faraday's law ∇×E=−∂t∂B​ (8)$$
🔗$$Equation 9. Ampere's circuital law ∇×B=μ0​(J+ε0​∂t∂E​) (9)$$
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You should also review the intuitive interpretation of divergence and curl.
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