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Kostik

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There's something very curious about Faraday's Law that results from considering a closed curve in space (and any surface whose boundary is that curve). Forget about conducting wires and EMFs: Faraday's Law gives the result of the integral of E along the curve in terms of the rate of change of flux through the surface. This is true for ANY curve, including an imaginary one without any actual wires, loops or conductors.

Consider any kind of magnetic field in space (such as the one around the Earth, or the Milky Way Galaxy, or just a hypothetical constant magnetic field), and assume it is constant in time. If there is no electric charge in the vicinity, there does not seem to be any source of any electric field (in the laboratory frame of reference) since the magnetic field is constant. But imagine a closed curve (say a circle, for simplicity) rotating about its diameter, or with a radius that is shrinking and expanding. By Faraday's Law, the integral of E along this curve is nonzero, so there ARE electric fields. In fact, since there are infinitely many possible curves, with different motions and distortions that can be imagined, there must be infinitely many electric field directions and magnitudes at every point in space, to produce all these various nonzero line integrals.

This doesn't make much sense. Can anybody explain it? Thanks.

Consider any kind of magnetic field in space (such as the one around the Earth, or the Milky Way Galaxy, or just a hypothetical constant magnetic field), and assume it is constant in time. If there is no electric charge in the vicinity, there does not seem to be any source of any electric field (in the laboratory frame of reference) since the magnetic field is constant. But imagine a closed curve (say a circle, for simplicity) rotating about its diameter, or with a radius that is shrinking and expanding. By Faraday's Law, the integral of E along this curve is nonzero, so there ARE electric fields. In fact, since there are infinitely many possible curves, with different motions and distortions that can be imagined, there must be infinitely many electric field directions and magnitudes at every point in space, to produce all these various nonzero line integrals.

This doesn't make much sense. Can anybody explain it? Thanks.

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