Some important equations

I found a cool html equation editor online based on a superset of the LaTeX markup language that allows me to code some important equations you should know about. You can find the site Here . You can also click on any equation to see its LaTeX source.

Fourier Expansion of a periodic function in three dimensions

$n(\vec{r}) = \sum_{\mathbf{G}}n_{\mathbf{G}}exp(i{\mathbf{G}}\cdot {\mathbf{r}}) \qquad \qquad (1)$

This equation is quite important, and I’m using it right now in my Solid State physics class to help define crystal structure. The constants $n_{\mathbf{G}}$ may be found by the following correlary function:

$n_{\mathbf{G}} = V^{-1}_C \int_{cell}dVn({\mathbf{r}})exp(-i{\mathbf{G}}\cdot {\mathbf{r}}) \qquad \qquad(2)$

Maxwell’s equations of electricity and magnetism

These bad boys will solve anything to to with E and M; including optics.

Name Equation
Gauss’ Law $\nabla \cdot \mathbf{E}=\frac{\rho}{\epsilon_0}$
Gauss’ Law for Magnetism $\nabla \cdot \mathbf{B}=0$
Maxwell – Faraday Equation $\nabla \times \mathbf{E}=-\frac{\partial \mathbf{B}}{\partial t}$
Ampere’s Law $\nabla \times \mathbf{B}= \mu _0\mathbf{J}+\mu_0\epsilon_0\frac{\partial \mathbf{E}}{\partial t}$

…more later

2 Replies to “Some important equations”

1. I like your site! I’ll tell you where these get funny, AC. I was making a tool demagnetizer the other month; just a spool of speaker wire and a 250 watt heat lamp as a resistor. What I found is that it is random whether or not the tool in the middle of the spool gets demagnetized or not. I found that this was because of the giant inductor i had just made… duh. So the solution was to put a variac in the circuit, and to start at 0 (optional), go to full, than back down to 0. neat, ah science. I also have since come up with an answer to one of your ponderings about pee in a wetsuit smelling bad. I believe humans, that did not think poop and pee smelled bad, died off. Maybe there is no great reaction chemically, but the mix of the smell of skin and pee triggers a response in the brain that says GO WASH.

1. lewis1286 says:

AC is funny. RF is even funnier. Buts its all in those four little equations. For lube: magnetic fields are simply a relativistic frame transformation of electric ones. I’ve been playing with ferrofluid lately, trying to get it to dance to Daft Punk via Arduino