Yes, that's correct. My motivation for asking this question is that the popular derivation of the formula for a generalized Lorentz transformation uses a rotation of the axes in this way, and it's assumed that they remain parallel.
Let me clarify.
Suppose S and S' have axes aligned with...
I tried posting this on the physicsstackexchange, but wasn't making any progress in understanding what's going on.
Suppose the axes in two coordinate systems S, S' are parallel. Now, suppose I rotate S through some angle ##\theta## and also rotate S' through the same angle ##\theta## It's not...
phyzguy,
A sketch would include four currents, two from the field (electrons move against the field, holes with the field) and two due to random thermal motions (electrons from P to N, holes from N to P). In equilibrium these effects cancel.
Consider a PN junction doped with say phosphorous on the N side, and Boron on the P side. Initially, there is an opportunity for the electrons just below the N conduction band to drop to the lower available energy states just above the P valence band. This leaves the N side positively charged...
To answer my own question, we are comparing the frequency measured by the ground observer -- who is at rest relative to the medium air -- with that measured by an observer moving with the siren and at rest relative to the air. Since they are both at rest relative to the air, they will measure...
Consider the situation where an observer at rest on the ground measures the frequency of a siren which is moving away from the observer at speed ##v_{Ex}##. Let ##v_w## be the speed of the sound wave. Let ##\lambda_0##, ##f_0##, ##\lambda_D##, and ##f_D## be the wavelengths and frequencies...
If what I have is a valid transformation, then I'm confused about what is calculating. Given the coordinates in S, does it give the coordinates in S(bar)?
I noticed that of course. But, isn't it true that the matrix gives S(bar) in terms of S? I don't see how the logic could be wrong. We give S(bar) in terms of S' and S' in terms of S, thus S(bar) in terms of S. I agree the formula is not a boost, but isn't it still correct?
Summary: The problem is to generalize the Lorentz transformation to two dimensions.
Relevant Equations
Lorentz Transformation along the positive x-axis:
$$ \begin{pmatrix}
\bar{x^0} \\
\bar{x^1} \\
\bar{x^2} \\
\bar{x^3} \\
\end{pmatrix} =
\begin{pmatrix}
\gamma & -\gamma \beta & 0 & 0 \\...
The formula for the integral is correct and produces the correct angular momentum. Yet, using the other coordinate system, I'm left with an integral which is divergent according to Mathematica. I mean the system with the origin as the midpoint between the charges. You can try writing down the...
Excellent answer, however in your example of the point mass, you are finding the angular momentum relative to 1. Where the particle itself is by placing it at the origin. 2. Some other location. In my example, I found the angular momentum relative to 1. The location of the electric charge. 2...
Relevant Equations:
Angular momentum density stored in an electromagnetic field: $$\vec{l}_{em} = \epsilon_0[\vec{r} \times (\vec{E} \times \vec{B})]$$
Electric field of an electric charge: $$\frac{q_e}{4\pi\epsilon_0}\frac{r - r'}{|r - r'|^3}$$
Magnetic field of a magnetic charge...
This question is motivated by Problem 7.12 in Griffiths Electrodynamics book. I have not included it in the homework section, because I have already solved it correctly. However, I question whether my solution which agrees with the solution's manual is correct.
Relevant Equations:
$$\Phi =...
Thanks for taking a look at it. The dimensions are correct. I'm using relativistic units, so |a| has units of 1/s. I'll email the professor and see if he is in agreement with our answers.