Homework Statement
A sphere of radius ##a## is submerged in a fluid which is flowing in the z-hat direction. There is some associated viscosity in the fluid which will exert a force on the sphere. Use symmetry to argue that the net force will be in the z-direction. Show that it will have the...
Homework Statement
"Evaluate: g^{\mu \nu} g_{\nu \rho} where ds^2 = g_{\mu \nu} dx^\mu dx^\nu , ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2 "
Homework Equations
None necessary, just a notation issue
The Attempt at a Solution
Just using raising and lowering rules, I imagine each raising and...
In the very first example of Feynman and Hibb's Path Integral book, they discuss a free particle with
\mathcal{L} = \frac{m}{2} \dot{x}(t)^2
In calculating it's classical action, they perform a simple integral over some interval of time t_a \rightarrow t_b.
S_{cl} = \frac{m}{2}...
Homework Statement
I'm solving a problem where a conducting pipe with a square cross section is being analyzed to find the potential everywhere in space. The pipe lays along the z-axis, so we're really concerned with the x-y plane. My issue isn't so much the general solution via separation...
We talked about the photoelectric effect in class today. A follow up conversation outside of class started among a few of us, and I'm having trouble sorting through literature on the subject to come to a clear conclusion.
It seems pretty intuitive that if I heat up a piece of metal, all of...
Apologies, I've worked with this problem some more and understand the units better.
To keep this system at a constant radius (which I give to be ~Bohr radius of hydrogen atom), I want to find out how fast a classical particle would have to move to maintain this radius.
Am I crazy to equate...
The idea being that I have two particles of opposite charge (particles implying the mass is negligible relative to the electric forces at play). One is fixed at the center, the other orbits around at a fixed radius. How would I go about solving for the angular velocity required to keep this...
V_{n}(r) = \int_{0}^{r}{A_{}(t) \, dt} \Rightarrow A_{n}(r) = \frac{d V_{n}(r)}{d r}
Maybe this is really elementary or really complex, but why does that work? Is volume defined this way, regardless of dimensionality? Or is there a deeper reason?
I recently came across the problem of finding the volume and surface area of a sphere of n-dimensions.
Two and three dimensions seemed to work out, but oddly enough it's one dimension that seems the strangest conceptually. How do you distinguish volume and surface area of a line?