Ah, so I'm also forgetting to add on atmospheric pressure. Thanks! So one final question, now if I have a shape where the area changes as a function of height, I can just substitute in A(y) and the rest stays the same, correct? I seem to recall that pressure at depth doesn't depend on the shape...
Yeah I feel like I'm pumping a little water to a height of 5 m, then a little to 5.1 m, etc. My other idea was that I need to perform an integral over the height:
$$E = \int_5^{10} \rho gr\,dr$$
where ##\rho## is the weight of water per ##dr##.
Homework Statement
Suppose you have a tank 10 m high. The tank is currently filled 5 m high with 1000 kg of water. How much energy does it take to pump in another 1000 kg of water from the bottom to fill the column to 10 m? (Ignore friction, etc.)
Homework Equations
E = m*g*h
The Attempt at...
Homework Statement
Given
$$L = \left(\nabla\phi + \dot{\textbf{A}}\right)^2 ,$$
how do you calculate $$\frac{\partial}{\partial x}\left(\frac{\partial L}{\partial(\partial\phi / \partial x)}\right)?$$
Homework Equations
By summing over the x, y, and z derivatives, the answer is supposed to...
Homework Statement
Suppose we have the standard rectangular potential barrier in 1D, with
$$
V =
\left\{
\!
\begin{aligned}
0 & \,\text{ if } x<0, x>d\\
V_0 & \,\text{ if } x>0,x<d\\
\end{aligned}
\right.
$$
The standard approach to solve for tunneling through the barrier is to match the...
Ah I think I finally understand. So if I had a voltage drop of 1 V across the entire structure, the electron's energy is 1 V, because I can call the exit the zero of energy, so the electron is 1 V higher (i.e. the Fermi level of the entrance side is 1 eV higher than at the exit). The potential...
Thanks for the reply. For the energy of the incoming electron, is there a simple way to relate it to say the voltage on the circuit? I don't think applying 1 V on a circuit actually gives the electron 1 eV of energy, because the electron isn't freely accelerating in vacuum.
Hello, I was trying to make a simple model of an electron tunneling through several potential barriers. The electron will flow through a conductor to a heterojunction of possibly semiconductor/oxide layers. I assume the electron is coming as a plane wave from the left with some energy E. We know...
I finally found the answer here: http://aapt.scitation.org/doi/10.1119/1.11582[/URL]. I don't know how he got it, because even using a diff eq solver I couldn't get that result. But I'll assume it's correct and I'm just missing something.
Homework Statement
Suppose we have a potential such that $$
V =
\left\{
\!
\begin{aligned}
0 & \text{ if } x<0\\
\mathcal{E}x & \text{ if } x>0, x<L\\
\mathcal{E}L & \text{ if } x>L
\end{aligned}
\right.
$$
for some electric field ##\mathcal{E}##. I'm trying to find the transmission...
Homework Statement
This isn't a homework question but something I'm working on that I thought should be simple. Two disks (area ##A## and thickness ##d##) are joined together and placed under a radiation heater in vacuum, so that one side of the top disk is heated with a constant power. Assume...