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1h
comment Why are our planets in the solar system all on the same disc/plane/layer?
@zibadawatimmy: I know many body gravitation problem is chaotic. Yet the solar system in the time scale of the earth life time until now is "relatively" stable. My question is what mathematical prohibition is there against a spherically distributed planet or dust orbital axis system with the same size orbit just like the solar system? Our solar planet system happens to be mostly planar. Is there a mathematical rationale stipulating the axis of rotation have all to be almost parallel and stable within the earth-life-time-until-now time scale?
2h
comment Why are our planets in the solar system all on the same disc/plane/layer?
@zibadawatimmy: Thank you for introducing me to the Oort cloud and supplying evidence of spherical distribution of orbits. Even with the dust and with collisions, why can dust not form, say, different annuli of different orientation at close distance to the sun? The rationale of chaos does not seem to be too convincing, since the planets in the solar system have been pretty stable with the current mutual distance. Does the orientation of the orbit so crucial even when we, say, make the mutual distance of those annuli to ten times that of the current planets?
4h
comment Why are our planets in the solar system all on the same disc/plane/layer?
@zibadawatimmy: Why do the planets belonging to two orthogonal axis of rotation have to be "discs" as you say and interact? The simplest counterexample is two concentric circles of different radii perpendicular to each other.
Aug
25
awarded  Tumbleweed
Aug
19
comment Total Momentum From a Standing Electromagnetic Wave
@MariusMatutiae: There was someone who, apparently without much tact, coincidentally perhaps at about the same time I pointed out the error of your answer, downvoted three of my questions and answers including this one, that are completely unrelated to each other, in quick succession within one minute, much shorter than it would have taken to even read any one of them. He did so stealthily and cowardly, not daring to leave a single comment pronouncing like a man his reason for downvotes . May I be so bold as to ask if that certain someone was you?
Aug
19
comment Total Momentum From a Standing Electromagnetic Wave
@MariusMatutiae: I notice that you have deleted your answer. I appreciate your intellectual honesty and courage in acknowledging your mistake.
Aug
18
revised Poynting Vector Volume Integral Inside a Cavity
Added EM resonance mode state description.
Aug
18
awarded  Critic
Aug
18
asked Poynting Vector Volume Integral Inside a Cavity
Aug
17
revised Total Momentum From a Standing Electromagnetic Wave
Specify more clearly my question.
Aug
17
comment Electromagnetic induction of an uniform magnetic field
That is better.
Aug
16
comment Electromagnetic induction of an uniform magnetic field
@Mr.T: "why should I need cylindrical symmetry in this situation?" The solution can be seen to be symmetric. Are you saying there is no need to use cylindrical symmetry to solve the problem or are you saying the solution should not be cylindrically symmetric? If your answer is the former, then yes, you do not have to use it to solve the problem. You can compute directly. It is only that the computation would be much more cumbersome. The utility of symmetry is to save labor. If your answer is the latter, then you are wrong. The solution will be cylindrically symmetric around the axis.
Aug
16
comment Electromagnetic induction of an uniform magnetic field
@Mr.T: What do you mean by "REQUIRE the symmetry of the solution to satisfy Maxwell equations"? Any solution, even without symmetry, should satisfy Maxwell's equation. Which "unsymmetric solution satisfies the Maxwell equation"? Asymmetric around the axis? Could you give such an asymmetric solution?
Aug
16
comment Electromagnetic induction of an uniform magnetic field
There is no need to impose boundary for $\mathbf E$. It is derived to be $\propto\frac{1}{r}$ outside of the infinitely long solenoid from the fact the magnetic field vanishes outside the solenoid.
Aug
16
awarded  Commentator
Aug
16
awarded  Student
Aug
16
revised Electromagnetic induction of an uniform magnetic field
added 155 characters in body
Aug
16
revised Electromagnetic induction of an uniform magnetic field
Read this question more clearly this time.
Aug
16
answered Electromagnetic induction of an uniform magnetic field
Aug
16
comment Total Momentum From a Standing Electromagnetic Wave
No apology is in order, @CuriousOne. In fact, I am sorry for my brusque reply. You question made me realize my question was not stated sufficiently clear. Thank you for your comments.