Natural sunlight is randomly polarized, meaning that the electric and magnetic fields do not oscillate in any preferred direction. They are indeed a superposition of orthogonal components, as you say. However this is not a superposition in the quantum mechanical sense. It is a superposition...
All that they are assuming is that ##\vec{\mu}## and ##\vec{B}## are not aligned. If they are aligned, then the equation does not apply, since then the cross product is zero, so that there is no change in ##\vec{\mu}##. But they are assuming that they are not aligned, and that the equation...
Gotta love the uniqueness theorem. So just to be clear, the boundary condition in combination with the fact that the potential satisfies Laplace's equation in the volume, imply not only that ##\Phi=##constant on the bounding surface, but also that ##\Phi=## constant throughout the entire...
This is out of Jackson's electrodynamics, problem 1.15.
I am trying to prove the theorem that if a number of surfaces are fixed in position and a given total charge is placed on each surface, then the electrostatic energy in the region bounded by the surfaces is an absolute minimum when the...
Where do I find a good comprehensive table of friction coefficients between various materials? I'd like, in particular, to be able to compare the coefficient of static friction between tungsten carbide and sapphire and that between sapphire and sapphire. Tables that I have found tend to have...
Let's see if I can get this right.
You want to analyze the motion of a rigid body. To do so we will do the usual thing and define two systems of coordinates: a body system and a stationary system. The body system is rigidly fixed in the body, meaning it translates and rotates with the body...
Start from the basics. Things exist. Now, of the things that exist, some of them interact with one another. Of the possible interactions that things have with one another, some involve accelerations of the participating things. Such interactions constitute a force by definition of force as...
The moment of inertia is generally used to calculate the kinetic energy of a rotating object.
The kinetic energy of your rod -- or any rigid body -- is composed of one part having to do with the rotation of the body about some axis fixed in the body and one part having to do with the...
Isn't it just that the center of mass is the weighted sum of positions with weighting factor equal to the mass at said positions, which is precisely what that integral term is, so that if you define the center of mass to be at the zero of coordinates, it will be zero?
I was just stuck on this problem for a while, but I think I got it now and hope that I can help someone else see how it goes.
The thing about the formula that is given in the textbook is that it is valid for any system of coordinates -- i.e. one need not assume that the coordinates are defined...
What happens if you look at the second system with the denser submarine from the perspective of its center of mass frame? Then by definition its center of mass is stationary.
What exactly do you mean by "exchange momentum" and why do you say that the denser submarine exchanges momentum with...