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White dwarfs with strong magnetic fields ($>$1MG) make up only about 10 per cent of the white dwarf population. A further few per cent have fields in the 10-1000 kG range (e.g.Liebert et al. 2003). So it is not clear that the Sun will end up as a "magnetic white dwarf" at all. The production of magnetic white dwarfs is thought to arise via at least two ...


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The hand-wavy way to do it is to consider a wave solution like the one below, and apply Faraday's law to loop 1, and Ampere's law to loop 2: If you make the loops narrow enough, i.e., their widths are $dx$, then $$\oint_1\!\vec{E}\cdot \vec{ds} = -\frac{d\Phi_B}{dt} \to \frac{\partial E_y}{\partial x} = -\frac{\partial B_z}{dt}$$ $$\oint_2\!\vec{B}\cdot ...


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OP asks (v1): How one can know the gauge field emerging from the local gauge invariance is actually the EM field? Assuming that OP is pondering about gauging theoretical models (rather than concerned with our actual world and phenomenological inputs) then the answer is: One cannot know. For starters, the gauge group $G$ could be different than $U(1)$. ...


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The only naturally occurring symmetry breaking radiation of this kind is the CMB. Unless you are talking about charged particles of more than approx. 1e19eV energy (in the CMB rest system), the effects are negligible, as far as I know. For those ultrahigh energy particles, however, this so called Greisen–Zatsepin–Kuzmin limit (GZK limit) forms a cosmic fog ...


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Since the emitter is a point, the wave will never get "flatter". It will always look like a dipole pattern (for the non-relativistic case, for the relativistic case the forward and backward lobes become asymmetric, I believe, with a strong amplification of the emission into the forward cones, which should also become narrower). I think you are mistaking your ...


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Expanding on Jan Dvorak's comment: When you change the magnetic field inside a loop, an emf (electromotive force) will be generated. Now if you have two loops, each of these will experience the same e.m.f. When you put them in series, you have a coil with two loops, or two coils with one loop. No matter which way you look at it the voltage across them ...


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The differential and integral forms of Maxwell's equations are truly equivalent; they are essentially the same set of equations. One can convert between the two using two mathematical theorems: Divergence Theorem (Wikipeda - Divergence Theorem) Stokes' Theorem (Wikipedia - Stokes Theorem) The divergence theorem states that the flux over a closed surface ...


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The wavelength does of course remain the same. Think about two circles (representing wavefronts) evolving over time. Their respective radii increase at the same rate, such that the distance between them (the wavelength) always stays the same. Now think about drawing a box of fixed size and placing it over the wavefronts. This represents your detector (or ...


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It is the electric field that does the work, not the magnetic field! When one has current in the loop, it can undergo a voltage drop or rise according to the inductance of the coil. Inductance relates to the electric field and its work. See: http://en.wikipedia.org/wiki/Faraday%27s_law_of_induction "The induced electromotive force in any closed circuit ...


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Propagation of electromagnetic waves on Earth is highly wavelength dependent, which is also true for the question whether the atmosphere has anything to do with it. What you are looking at is actually a formula for the geometric attenuation (aka free space or path loss), which has absolutely nothing to do with the atmosphere. As ACuriousMind points out, your ...


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The idea is that since the steel beam has conduction electrons that are free to move, the movement of the charges in a magnetic field causes a magnetic force to act. The magnetic force causes the electrons to accumulate at one part of the curved surface of the rod, thereby creating a potential difference. The charges keep accumulating till the potential ...



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