Recent content by RoyalCat

I think it's because the average momentum is 0 (Closed orbit), so the time-average of the momentum squared (Which is what actually enters the equation), is exactly the variance in the expectation value of the momentum.

In Dirac's "The Principles of Quantum Mechanics", in chapter V on the equations of motion Dirac proceeds with a line of reasoning that is something along the following lines (I've modified it a bit to coincide with what's taught in the course I'm taking) 1. We assume that the motion...

I find it a stretch that we're simply ignoring the contribution of the dipoles to the potential energy. There must be some other explanation as to why we're only considering free charge in the integration. The matter isn't how to rewrite the equation in terms of the free charge, but why it...

Thanks for the reply, but that wasn't quite what I was asking. The problem for me is understanding why we need only take account of the free charge when calculating the integral. We know that in a vacuum, the total energy is given by \tfrac{1}{2}\int \rho \phi dV If we interpret the dielectric...

The energy density function for the electric field in vacuum is u=\dfrac{\epsilon_0}{2}E^2 And the cited textbook result for the energy density inside a dielectric is: u=\dfrac{\epsilon_0 \epsilon_r}{2}E^2 Now, one way to reach the upper formula is to look at the energy as...

You were told explicitly not to involve any physics in the dimensional analysis. Throw out everything you know about collisions and use dimensional analysis. Do you know how to perform dimensional analysis? If not, then refer to this text, scroll down to page 3-4 or so if you're familiar with...

Consider the fact that the upper mass, confined by the string l1, is forced to move in a circular arc. What must the net force on it be?

Due to a typo in the TeX, the lambda didn't show up in the integral. Don't take everything you're told by fiat. Think things through. What I posted earlier was nonsense. I said that the total charge is the length of the rod. That's gibberish. Please think the problem through, I've given you all...

You know that \frac{dq}{dx}=\lambda Therefore, Q_{total}=\int^{\ell}_0 \lambda dx

You are told explicitly, \lambda = kx^2 So stating \lambda =\frac{Q}{\ell} is a mistake! The total charge is a quantity you need to determine the numerical value of k

This is a conceptual question in special relativity. Let's say we have 2 cyclists riding parallel to each other, separated by a distance D, at a constant velocity directed along the x axis, v. Cyclist A has a laser, and he points it at cyclist B and presses the button so that a short pulse...

How springy would such a spring be? :p

You have two second-order differential equations, one for the motion in the x plane, and another for the motion in the y plane. you are missing two initial value constants.

No, that is not true. Write out Newton's Second Law for both, and you will see that the equations for the displacement of each are coupled! The force on mass 1, depends on the position of mass 2, and vice versa. :) The meaningful coordinates that can be defined, in this case, are the relative...

Please reconsider everything you've posted. It is wrong from the very first line (c2=1/(μ0ε0)). It shows a deep confusion with respect to the relevant concepts. I urge you to take the subject up seriously and methodically, you seem to me like you're very passionate about the subject and about...