iScience92

studiot: take a 3dimensional wave for example, or... a plane wave you still have 4 indep. var.s but in my optics class we've turned the original wave function into a second order differential.

Anyone have any recommendations for a decent 3D E-field simulator?

We know the general solutions (wave equations) for a variety of waves. Why is it preferable to express them as second differentials?

One day I applied Lorentz's Law on a charge inside the coil of a speaker. I found that in any given instant, the force felt by a particle was always radially outward, not along the coil wire. So i claim, either there is a relationship between the two laws, in which case, i'm trying to derive the less fundamental to the one more so. Or, there is another "law" of interaction going on that i don't know about, in which case, please inform me so.

Oh! PS, well, more like pre-script... my goal is to derive faraday's induction law from lorentz force law

[math]\vec{F}=q\vec{v}\times\vec{B}[/math] [math]\frac{d\vec{F}}{dq}=\vec{v}\times\vec{B}[/math] [math]\int\frac{d\vec{F}}{dq} \cdot ds=\int(\frac{d\vec{s}}{dt}\times\vec{B}) \cdot ds[/math] from here, I went about it two different ways: 1.) Here I assumed everything was at right angles and got rid of all the vectors and vector products [math]\varepsilon=\int \frac{ds}{dt}B ds=\int \frac{ds}{dt}B \frac{ds}{dt}dt[/math] By u substitution [math]u=\frac{ds}{dt}, du=dt[/math] [math]\varepsilon=\int B(u^2)du=\frac{Bv^3}{3}[/math] where v = ds/dt That was the first way i went about it, but i didn't feel any closer to Faraday's law. 2.) Here I left the vectors alone on the RHS; I figured since [math]\hat{v}[/math] and d[math]\hat{s}[/math] were perpendicular, the quantity ([math]\vec{v}[/math]s) would be a time derivative of the area formed [math]\varepsilon=\int\frac{ds}{dt}B ds=\int(\vec{v}\times\vec{B}) \cdot d\vec{s}=\dot{A}B[/math] [math]\varepsilon=\frac{BA}{dt}[/math] don't know where the minus sign is; probably was supposed to do something with the cross product, but didn't know what. Well I got alot further with the second "method," but is this a valid derivation? and what went wrong with the first method?

I'm reading from Griffith's Intro to E&M as an intro to the topic/phenomenon; hence i was working with a simplified analogy. "Orbital momenta"? Considering an electron orbiting on a 2-D plane (the simplified analogy given in the book), i intuitively understand what the "oritentation of orbit" refers to, but in actuality, when you say that an orbital can have a finite set of orbital momenta in any [math]\hat{r}[/math], i take this to be a time averaged information, is this correct? If not, then at any given time t, how exactly is the orientation defined? But why is the paramagnetic effect always stronger than the diamagnetic one? Is there a qualitative explanation?

Please confirm & answer the following: An atom exposed to an external B-field will experience both a torque on its orbitals (paramagnetism), and a change in orbital velocities and thereby a change in the magnetic momenta of the orbits (diamagnetism). When the atom has all paired electrons, the net torque is zero so the phenomenon resulting from the change in orbital velocity dominates. But, when the atom has an unpaired electron, the net torque on that orbital is non-zero. Question: So do these orbitals physically re-orient themselves to align with the Bexternal? but the diamagnetic effect/influence is still present. Question: For atoms with unpaired electrons, why does the paramagnetic effect always win?

Hi, I was hoping to get some pointers/ references for the following: I'm trying to learn about the force that an electron experiences while in a conductor. When bound to a conductor, it's essentially in potential well. My goal is be able to model this potential well to manipulate it. I'm trying to get an electron to physically leave its conductor but i don't want to just blindly "do it," i want to understand it. Thanks in advance