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Thanks for the input; it means a lot. Anyone other opinions?

I'm basically asking if I should apply for the physics major, then change to something else, or cut the middleman out and apply directly to my desired major.

Hi, I attended college for two years at a large state university. In my fifth semester, due to financial complications, mid-semester I was forced to return home and get a full-time job. I'm looking to apply to another institution as a transfer student. I've earned mostly A's, took honors...

I'm sorry I'm not really sure how to do that.

Would it be ##dr=(r\rho)dV##?

Problem: Material scientists have discovered a new fluid property called "radost" that is carried along with a fluid as it moves from one place to the next (just like a fluid's mass or momentum). Let ##r(x,y,z,t)## be the amount of radost/unit mass in a fluid. Let ##\rho(x,y,z,t)## be the...

One last thing: ##2q## comes from the fact that \int_0^r \rho_n (\vec{r}) d\tau=\int \int \int 2q \delta^3(\vec{r})r^2 sin\phi \ dr \ d\theta \ d\phi=2q \int \int \int \delta^3(\vec{r})r^2 sin\phi \ dr \ d\theta \ d\phi = 2q \cdot 1 = 2q Correct?

Darn, so close. So then I have ##Q_{enc}=2q+\int_0^r \rho_e(\vec{r})d\tau##. And the integral is then ##\int_0^r \rho_e(\vec{r})d\tau=\int_0^{2 \pi} \int_0^{\pi} \int_0^{r}(-\frac{8q}{\pi {a_0}^3}e^{-4r/{a_0}})r^2sin\phi \ dr \ d\theta \ d\phi##.

I don't know if you saw the edit to my last post, but I realized it was wrong right after I posted it. But the charge enclosed in the Gaussian surface should be ##Q_{enc}=2q+\int_0^r \rho_e(\vec{r}) dr##, I believe.

Okay thanks! So I'm getting ##\vec{E}=\frac{1}{4\pi \epsilon_0}\frac{q}{r^2}\hat{r}## as my final answer. (Fixed the error in my previous post as well.) EDIT: Oh wait... pretty sure this is wrong because I didn't account for the electron cloud only partially contributing to the enclosed...

Oh right! So I'll wind up with an equation for the electric field ##\vec{E}## as a function of ##r##. So I start with the LHS of Gauss's law: ##\oint \vec{E} \cdot d\vec{A}## ##\vec{E}## and ##d\vec{A}## will be parallel, so we get ##\int |\vec{E}|d\vec{A}##. And since the magnitude of...

Wouldn't the only way to enclose all of the charge of the electron be to have a sphere with an infinite radius act as our Gaussian surface?

Problem: In a neutral He atom consisting of a positively charged nucleus of charge ##2q## and two electrons each of charge ##-q##, the volume charge density for the nucleus and for the single electron cloud are respectively given by \rho_n(\vec{r})=2q\delta^3(\vec{r}) and...

So ##f(x,y,z)=y-x^2##?

More specifically I meant, how would you find ##f## analytically from this info given?