Recent content by russdot

Ah yes, so since e^{A} is defined with a power series e^{A} = 1 + A + \frac{A^{2}}{2!} + \frac{A^{3}}{3!} + ... and A commutes with itself then A would commute with e^{A} Thanks!

If A is an operator, is it correct/allowed to say: Ae^{iA} = e^{iA}A Thanks

Homework Statement This is more of a general question. If I have two different integrals that equal the same value, is it valid to equate the integrands? Homework Equations \int P(\theta,\phi)d\Omega = N \int Q(\theta',\phi')d\Omega' = N Where N is a constant and d\Omega = sin\theta...

JesseM, Thanks for the reply, those links helped a lot :)

If one was in a spaceship at rest in frame K and sees an evenly-distributed number of stars around them, what would the distribution of stars look like if you were traveling at relativistic speeds (frame K')? I'm conflicted because I've seen animations online that seem to illustrate the stars...

Homework Statement \frac{1 + \sqrt{\frac{1}{1 + \left(\frac{s}{u}\right)^{2}}}}{1 - \sqrt{\frac{1}{1 + \left(\frac{s}{u}\right)^{2}}}} Should equal \left(\sqrt{1 + \left(\frac{u}{s}\right)^2} + \left(\frac{u}{s}\right)\right)^{2} Homework Equations above The Attempt at a Solution...

For the magnetic field of each loop (along Z axis), I get: \vec{B}(z) = \frac{\mu_{0}}{4 \pi} \int \frac{\sigma 2 \pi \omega x'^{2} (\hat{\phi} \times \hat{r})dx'd\phi}{x'^{2} + z^{2}} where \hat{\phi} \times \hat{\r} = \hat{k}cos\psi + \hat{R}sin\psi (\psi is the angle between\vec{r} =...

Ah yes, I really should eat some food... but since \vec{I} = \lambda \vec{v} and \lambda = \sigma 2 \pi dr and \vec{v} = r \vec{\omega} then \vec{I} = \sigma 2 \pi \vec{\omega} r dr, correct?

Hi gabbagabbahey, Thanks for the tips, I'm still getting used to the LaTeX notation. marcusl, Ok, and then each infinitesimal loop will have a current I = \sigma 2 \pi R dr.

Homework Statement A thin disc of radius R carries a surface charge \sigma. It rotates with angular frequency \omega about the z axis, which is perpendicular to the disc and through its center. What is B along the z axis? Homework Equations General Biot-Savart law: B(x) =...

Yes, you're right. The form I used was ambiguous, sorry about that! I guess I just jumped right to using R^{2}sin\theta' d\theta' d\phi as the surface area element. I have solved the problem though, thanks for the assistance!

Well d^{3}x' turns into r^{2}sin\theta dr d\theta d\phi and since r is constant at R (spherical shell) then an R^2 comes out of the integral and cancels the R^2 in the denominator from the charge density rho = Q / (4 pi R^2). I also figured out the problem, after integration: V(x) =...

[solved] Potential inside (and outside) a charged spherical shell Homework Statement Use the integral (i) to determine the potential V(x) both inside and outside a uniformly charge spherical surface, with total charge Q and radius R. Homework Equations (i) V(\vec{x}) =...

Great, thanks! I'm assuming if the rms equation is correct, then the mean value equation is also correct..

Hello, Given a particular charge distribution p(r) = p_0*exp(-r^{2}/a^{2}), I was wondering if the proper way to calculate the mean radius <r> would be \intp(r)*r*p(r) dV ? Which would make <r^{2}>^{1/2} = (\intp(r)*r^{2}*p(r) dV)^{1/2}, correct?