The assignment has already been turned in. I ended up just not using the given formula. Got the correct answer, even if not really in the correct way. Thanks though.
Homework Statement
Assume that an electron is a sphere of uniform mass density
\rho_m=\frac{m_e}{\frac{4}{3} \pi r_e^3}, uniform charge
density \rho_e=\frac{-e}{\frac{4}{3} \pi r_e^3}, and
radius r_e rotating at a frequency \omega
about the z-axis. m_e=9.109*10^{-31} kg and
e=1.602*10^{-19} C...
That's what's throwing me off. There is no "physical system" as I have come to understand it. All I'm given is what I wrote above. I understand that to calculate perturbations in general, you use <Psi|H'|Psi>, but that gets me back to needing a wavefunction to operate on. All I have is this...
Homework Statement
"Determine a surface temperature value for the Sun from the angular diameter of the Sun and the solar constant."
Homework Equations
L=4π(R^2)σT^4
The Attempt at a Solution
At this point my only stumbling block is I don't understand the relationship between the solar...
You're doing the right hand rule incorrectly. Your thumb needs to be pointing in the direction of the magnetic force. When you do this and orient your fingers to point in the direction of i in the picture, you will see that they curl down, in the -y direction.
As far as graphing, you need to recognize that F is a function of r, F(r). So you treat r as you would any variable and graph it with the values for k and q given: http://www.wolframalpha.com/input/?i=Plot%5B%28%28%288.988%C3%9710^9%29%2817*10^-9%29%289*10^-9%29%29%2F%28r^2%29%29%2C{r%2C0%2C25}%5D
I realize that. My question is, am I right in saying that there are no residues? I'm thinking this is some form of a "residue at infinity" example, in which case there are new rules, but I don't understand this enough to tell.
In terms of the functions x and y, slope=y'/x'
y'(\theta)=f(\theta)*Cos(\theta)+f'(\theta)*Sin(\theta)
x'(\theta)=-f(\theta)*Sin(\theta)+f'(\theta)*Cos(\theta)
Divide y' by x', switching the order of terms in x', and you have the given expression for slope.
Ok, I've had an idea. If I let x=z3, then the denominator becomes 1-x. Nice, since the series representation of \frac{1}{1-x} is well known. Now I'm just not sure what this change of variable does to the numerator. z5=z3*z2, but I'm not sure how to write z2 in terms of z3. My brain fails...
You are correct in saying that the product and chain rules are needed, however you neglected to apply the product rule.
f(t)=t*e2-7t
f'(t)=t*d/dt(e2-7t)+d/dt(t)*e2-7t