Recent content by Smacal1072

Hi All, Again, thanks to all the Physics Forums gurus. I posted a question about a year ago concerning the finite propagation speed of information and electrostatic forces between charges, which seemed confusing. I still was hoping to resolve it, so I simplified it a bit :). Imagine a...

Ok, I think I have a piece of the puzzle. I was not considering the Lorentz force on each particle relativistically. The relativistic Lorentz force is actually: \mathbf{F} = \gamma q(\mathbf{E} \mathbf{v} \times \mathbf{B}) Where \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} But...

Griffiths derives the \mathbf{E} field of a point charge moving with constant velocity from the Liénard–Wiechert potentials in chapter 10.3: \mathbf{E}(\mathbf{r},t) = \frac{q}{4\pi\epsilon_{0}} \frac{1-v^{2}/c^{2}}{\left(1-v^{2}\sin^{2}{\theta/c^{2}}\right)}\frac{\hat{\mathbf{R}}}{R^{2}}...

Yes, thanks dauto, I misspoke there. Pretty much. In relativistic electrodynamics, the \mathbf{E} field and \mathbf{B} field are all the result of the same underlying thing. All magnetic effects can be viewed as electrical effects as viewed in a different frame of reference. However, just note...

Hi All, I've been reading Griffiths E&M and Feynman Lectures (vol 2, E&M), and it made me think about a gedanken that I'm trying to resolve. I'm pretty sure once I really peruse the chapters on the relativistic formulation it'll make sense, but I'm impatient :biggrin: I have two identical...

The best way to understand the magnetic field as a relativistic E field is with the example of a current-carrying wire. Griffiths explains it best: "A current-carrying wire that is electrically neutral in one inertial system will be charged in another." Suppose you put a "stationary"...

Hi All, Thanks again to all the great mentors and contributors to this forum. I wanted to ask a question about the Gauss's law/Ampere's law equations in Maxwell's Equations: \nabla \bullet \textbf{E} = \frac{\rho}{\epsilon_0} \\ \\ \nabla \times \textbf{B} = \mu \left( \textbf{J} + \epsilon...

Hi Jano, Thank you for taking the time to respond - I considered your idea of looking at the velocities and elongations along the anti-diagonal, and you are right, it is completely analogous to the 1D case where energy is conserved.

Jano, your analysis is completely clear - A 1D wave pulse interfering with a 1D wave pulse will conserve energy, since all of the kinetic energy of both waves' motion is being converted into potential energy in the region of overlap. However, the system I was imagining was two-dimensional. I...

I agree, I think that the energy density can be misleading in systems like this - I think the total system energy is a better metric. My point of confusion is that the total energy of the system appears to be different before and after the wave pulses interfere (between the first and second...

Hi All, First off, thanks to all the old hands at physicsforums, you guys are truly an amazing resource. I was thinking about a system today that at first glance, appears to violate local conservation of energy for two mechanical wave pulses interfering with each other. Consider a...

jambaugh - I didn't realize that by covering the emitter we were trapping the photon gas in the cylinder. I can see now that compressing the piston will require more work than the amount that would be extracted from the expansion, so the temperature would rise. Thanks for your comment.

Yes, I'd assume the piston is a vacuum. Also, to keep it simple, let's assume the cylinder is on Earth and vertical, so that gravity will pull the mirror back down.

Hi All, First off, everyone on this forum is amazing. Period. Second, I had a thought experiment the other day that was interesting and was hoping you could comment on it: The System: Imagine an infinitely long hollow cylinder in one direction, made of a metal (perhaps aluminum). At the...

I guess that's the point of confusion then. I did a little digging, and found an excerpt from Maxwell's "Theory of Heat" (pg 300-301): This sort of summarizes one of the apparently paradoxical situations we thought up earlier. (I honestly just stumbled upon this today). Since we know that 2...