Does anyone know of a reference that uses only Maxwell's equations to solve the problem of a moving point charge (non relativistically) and the corresponding Magnetic field? I want a solution that does not involve doing a Lorentz transformation. Beginning to think it cannot be done!
This makes me think about another problem that is sort of interesting. A child on a swing. How does the child get the swing going higher and higher when there is nobody pushing him?
Does anyone know where I can find a derivation of the magnetic field of a moving point charge from Ampere's Law? (not the Biot Savart law, but directly from Ampere's law).
was there space before the big bang?
I tend to think of mass not only influencing space, but creating it. so at the big bang did space race out ahead of mass or just ride along with it?
Suppose you had 2 equal point masses, one at r and one at 2 r. The moment of inertia is m rsq + 4 m rsq or 5 m rsq. If I place both masses at the center of mass at 3/2 r, then the moment of inertia is 2 m x 9/4 rsq or 4.5 m rsq. I think this is where the confusion lies?
proposed problem
This might help clear up the question. Suppose a force F is applied perpendicular to the rod at a distance of 1/2 the location of the center of mass from the center. What is the angular acceleration?
Interesting thought experiment, as the speed of light is slower in a medium, it is only c in free space. For example, the speed of light in a metal is zero. Seems like we could theoretically create a material where the speed of light is very slow. You might think about how that would be done.
You are on the right track, I see it as torque = (moment of inertia) x angular acceleration.
S is force, r is radius, 1/2 m rsq is moment of inertia, and a is linear acceleration, a/r is angular acceleration.
My suggestion:
First take second derivative of x with respect to t to get acceleration which we will call z.
Then use dz/dx = (dz/dt)/(dx/dt)
Looks messy, but technically correct. In the final result, substitute for x where it appears.
One of the things I never really thought about, but learned recently. Perhaps this is obvious to many. The relative sizes of the sun and the moon, and their relative distances from Earth make it possible for the moon to "almost" completely block out the sun during a total eclipse, allowing us to...
Stars and galaxies that are further away from us are moving away faster, based on the red shift. What is the relationship between the maximum velocity of the furthest ones, as a fraction of the speed of light, and the mass of the universe? If we extrapolate the velocity up to the speed of light...