Recent content by Z90E532

Homework Statement Given a wave function that is the super position of the two lowest energies of a particle in an infinite square well ##\Psi = \frac{\sqrt{2}}{\sqrt{3}}\psi _1 + \frac{1}{\sqrt{3}}\psi _2##, find ##\langle E \rangle##. Homework EquationsThe Attempt at a Solution I'm not sure...

Homework Statement Given the sequence ##\frac{1}{2}(x_n + \frac{2}{x_n})= x_{n+1}##, where ##x_1 =1##: Prove that ##x_n## is never less than ##\sqrt{2}##, then use this to prove that ##x_n - x_{n+1} \ge 0## and conclude ##\lim x_n = \sqrt{2}##. Homework EquationsThe Attempt at a Solution...

Yeah, I think I was just having a brain malfunction... it's pretty late here. I think this is the right approach: For a surface charged sphere: ##\vec{E} = \frac{R^2 \sigma}{\epsilon _{0}r^2}## then we have ##V = - \int ^{R} _{\infty} \frac{R^2 \sigma}{\epsilon _{0}r^2} dr =\frac{R^2...

I corrected my mistake I think, but I still am not sure how to find the surface charge density from only the voltage. I think my brain stopped working.

Homework Statement Find the magnetic dipole moment of a spinning sphere of voltage ##V## and radius ##R## with angular frequency ##\omega##. Homework EquationsThe Attempt at a Solution To find the dipole moment, we need to do ##I \int d \vec{a}##, which would be ##I 4 \pi R^2 \hat{r}##, but I...

The standard one: http://mathworld.wolfram.com/LeftInverse.html I see what you're saying about ##S##, I didn't realize that at first.

Homework Statement Let ##S ## be a cylinder defined by ##x^2 + y^2 = 1##, and given a parametrization ##f(x,y) = \left( \frac{x}{ \sqrt{x^2 + y^2}}, \frac{y}{ \sqrt{x^2 + y^2} },\ln \left(x^2+y^2\right) \right)## , where ##f: U \subset \mathbb R^2 \rightarrow \mathbb R^3 ## and ## U = \mathbb...

Well, when I say 50%, I mean I went over the parts that I thought were important. I don't feel like finding the book again, but I did the chapters on limits, continuity, differentiability, integration etc. I've studied linear algebra, so that's not really a problem. I could definitely use some...

I'm a physics student trying to get a more in-depth understanding of math. A few weeks ago, I started studying from two textbooks, Spivak's Calculus on Manifolds and Hubbard's Vector Calculus, Linear Algebra, and Differential Forms. So far, the stuff from Hubbard's text is pretty straight...

I have a question regarding the usage of notation on problem 2-11. Find ##f'(x, y)## where ## f(x,y) = \int ^{x + y} _{a} g = [h \circ (\pi _1 + \pi _2 )] (x, y)## where ##h = \int ^t _a g## and ##g : R \rightarrow R## Since no differential is given, what exactly are we integrating with...

Sure we can get it to work with just ##dm = \frac{M}{A} dA = \frac{M}{A}R d \theta 2 \pi r##, but this contradicts what I had found for it, which was (say ##\rho = 1##)##dm = 2 \pi r dz = 2 \pi (R \cos \theta )(\frac{R d \theta}{\cos\theta})## which leads to the integral after ##r^2## is...

I didn't but I shouldn't have to, right? It's a spherical shell of zero thickness.

Homework Statement Find the moment of inertia of a spherical shell Homework EquationsThe Attempt at a Solution So I've been mulling over this for about two hours now and haven't figured out where I've made a mistake. Here's what I've done: I know I can do the integral by doing ##\int ^{r}...