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| Tags: magnetostatics |
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#1
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**GR and Magnetostatics**
GR accounts for the magnetostatic force quite simply, the key being the relation, Length=(G/c^2)*Mass. , G is Newton's, so that the Mass of the Sun is 1.47 km. That is explained in Weinberg's "Grav&Cosmo" pg.181, using R = r - MG on the Schwarzschild Solution. That 1.47 km has been confirmed by light deflection. The next thing to understand is Guv =Tuv means Curvature (Guv) increases as the Energy Density (Tuv) increases, so that two repelling magnetics increase Tuv when forced together, while Tuv decreases when attractive magnets are brought together. Consider the following diagram, using points p1 and p2 to designate locations in a field free space, "s=n" is a bar magnet, and X, La and Lr are the lengths, measured by light rays separating the positions, of p1,p2 and "s=n", "n=s" and "s=n", "n=s", respectively though exagerated, with the bar magnets set exactly at p1 and p2, then the Length in the attractive couple "La" is less than the distance in the repulsive couple "Lr", due to Guv=Tuv, p1---------X---------p2 s=n-----La-----s=n s=n----------Lr-----------n=s From that we can find the energy stored, using from GR from above, Length(L) = (G/c^4)*Energy(E), and E = K*L , K=c^4/G . La - X = -DX , Ea= -K*DX , (attractive) Lr - X = +DX , Er= +K*DX , (repulsive) with the Energy Ea removed, from the Tuv as the attractive bar magnets are moved from infinity to p1 and p2, and the Er is the Energy put into the system to move the repelling magnets to p1 and p2 from infinity and the above DX are the result of Tuv on the Curvature Guv. The Magnetostatic "Force" is measured by changing the Energy of the system, and likewise the Curvature change becomes real, such that D^2(X) =/=0. The challenge is to determine how the metric g_uv varies to produce the magnetostatic energy and forces above. Regards Ken S. Tucker kxsxt8 |
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#2
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On Jul 7, 12:30 pm, "Ken S. Tucker" wrote:
[...] The Magnetostatic "Force" is measured by changing the Energy of the system, and likewise the Curvature change becomes real, such that D^2(X) =/=0. The challenge is to determine how the metric g_uv varies to produce the magnetostatic energy and forces above. Regards Ken S. Tucker kxsxt8 If someone stole the "3" from your keyboard I think it is OK to write 1+2 as an exponent. )http://www.sm.luth.se/~urban/master/Theory/3.html 39 items, totalling 240.5 KB for the dial-up challenged Gudonya, Sue... |
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#3
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On Jul 7, 9:48 am, "Sue..." wrote:
On Jul 7, 12:30 pm, "Ken S. Tucker" wrote: [...] The Magnetostatic "Force" is measured by changing the Energy of the system, and likewise the Curvature change becomes real, such that D^2(X) =/=0. The challenge is to determine how the metric g_uv varies to produce the magnetostatic energy and forces above. Regards Ken S. Tucker kxsxt8 If someone stole the "3" from your keyboard I think it is OK to write 1+2 as an exponent. )http://www.sm.luth.se/~urban/master/Theory/3.html 39 items, totalling 240.5 KB for the dial-up challenged Gudonya, Sue... All you need to do is recognize the effect of energy density on curvature to see how GR explains magnetism via the spacetime field. Even I can understand it! Ken |
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#4
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On Jul 7, 1:26 pm, "Ken S. Tucker" wrote:
On Jul 7, 9:48 am, "Sue..." wrote: On Jul 7, 12:30 pm, "Ken S. Tucker" wrote: [...] The Magnetostatic "Force" is measured by changing the Energy of the system, and likewise the Curvature change becomes real, such that D^2(X) =/=0. The challenge is to determine how the metric g_uv varies to produce the magnetostatic energy and forces above. Regards Ken S. Tucker kxsxt8 If someone stole the "3" from your keyboard I think it is OK to write 1+2 as an exponent. )http://www.sm.luth.se/~urban/master/Theory/3.html 39 items, totalling 240.5 KB for the dial-up challenged Gudonya, Sue... All you need to do is recognize the effect of energy density on curvature to see how GR explains magnetism via the spacetime field. Even I can understand it! Is that because you omitted the "challenging" part? "Tensors and pseudo-tensors" http://farside.ph.utexas.edu/teachin...s/node120.html Sue... Ken |
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#5
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On Jul 7, 11:15 am, "Sue..." wrote:
On Jul 7, 1:26 pm, "Ken S. Tucker" wrote: On Jul 7, 9:48 am, "Sue..." wrote: On Jul 7, 12:30 pm, "Ken S. Tucker" wrote: [...] The Magnetostatic "Force" is measured by changing the Energy of the system, and likewise the Curvature change becomes real, such that D^2(X) =/=0. The challenge is to determine how the metric g_uv varies to produce the magnetostatic energy and forces above. Regards Ken S. Tucker kxsxt8 If someone stole the "3" from your keyboard I think it is OK to write 1+2 as an exponent. )http://www.sm.luth.se/~urban/master/Theory/3.html 39 items, totalling 240.5 KB for the dial-up challenged Gudonya, Sue... All you need to do is recognize the effect of energy density on curvature to see how GR explains magnetism via the spacetime field. Even I can understand it! Is that because you omitted the "challenging" part? "Tensors and pseudo-tensors"http://farside.ph.utexas.edu/teaching/em/lectures/node120.html GR provides the ability to simply connect magnetism with the spacetime field conceptually, using fairly primitive math. The best solutions to the "challenge" (IMO) use asymmetric metrics that become evident in rotation, but 1st is to get the concept written out, then go to proofs. Regards Ken S. Tucker |
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