# Search results

1. ### Question Regarding Electromagnetic Fields in Special Relativity

According to the http://en.wikipedia.org/wiki/Biot-Savart_Law" [Broken], the equation for the magnetic field around a charged particle moving with constant velocity is \mathbf{B} = \frac{1}{c^2} \mathbf{v} \times \mathbf{E} But then...
2. ### Maxwell's equation and Helmholtz's Theorem

I am trying to find the magnetic field around a moving point particle. I have already found the curl. The only step remaining is to use Helmholtz's theorem. I am using http://farside.ph.utexas.edu/teaching/em/lectures/node37.html" [Broken]. I am going to use equation 300, but I am not sure...
3. ### Help with Newtonian Potentials for Helmholtz Decomposition

I'm trying to find a divergenceless vector field based on its curl, and discovered that I could use a http://en.wikipedia.org/wiki/Helmholtz_decomposition" [Broken], and the article I found on this didn't make much sense to me. First, can someone confirm that the dimension referred to in the...
4. ### Newtonian potential in Helmholtz decomposition

I'm trying to find a divergenceless vector field based on its curl, and discovered that I could use a http://en.wikipedia.org/wiki/Helmholtz_decomposition" [Broken], and the article I found on this didn't make much sense to me. First, can someone confirm that the dimension referred to in...
5. ### Solving Differential Equations Involving Vector Fields

Given the curl and divergence of a vector field, how would one solve for that vector field? In the particular case I would like to solve, divergence is zero at all coordinates.
6. ### Operator questions

I'm looking into vector calculus right now, and I have a few questions. * is the dot operator What is the difference between \nabla * F and F * \nabla ? What is \nabla ^2 F, where F is a vector field?
7. ### Curl and vector fields

Given an equation describing the curl of a vector field, is it possible to derive an equation for the originating vector field? The divergence of the field is known to be zero at all points
8. ### Curl reversibility?

I'm working with Maxwell's equations, and I have found the curl of a magnetic field at all points. How can I figure out what the magnetic field is at those points?
9. ### Question about Lie Brackets in Group Theory

What does it mean when a Lie Bracket has a subscript + or - directly after it? I found this notation in http://en.wikipedia.org/wiki/Special_unitary_group" [Broken] under the fundamental representation heading Those are Lie Brackets, right? I know Lie Brackets are being used elsewhere in...
10. ### Fresnel Equations Question

Is there a generalized Fresnel equation for the reflection of light with arbitrary polarization (between p and s)?
11. ### Statistics- Degrees of Freedom

If I flip two coins at once and don't care which one is heads in the case of a head and a tail, how many degrees of freedom are there?
12. ### Meissner Effect- magnetic focusing

Could superconductors be used to focus a magnetic field? For instance, lets say we have a superconducting cylinder and we place a wire coil in one end. If we put current through the wire, could it be used as a more effective Gauss gun than the same coil without the superconducting cylinder?
13. ### Quadratic Recurrence and the Mandelbrot Set

I am currently studying the Mandelbrot set, and have a question about one of the statements on http://mathworld.wolfram.com/QuadraticMap.html" [Broken]. It says the recurrence for the Mandelbrot set "is not in general solvable in closed form." What does this mean?
14. ### Convergence of Series

What is the name of the test that allows you to find convergence for such series as (0,1,0,1,0,1...)? It makes that series converge to 1/2
15. ### Mandelbrot Set- definitive point testing

For those of you not familiar with the mandelbrot set, it is the set of all complex numbers c for which the following transform remains finite for an infinite number of iterations: z --> z^2 + c z is 0 for the first iteration My question is this: How can I conclusively determine...
16. ### Quantized spacetime and Special Relativity

How does special relativity affect a quantized spacetime? Specifically, how can time and space be quantized the same way for all observers?
17. ### Question- abstract index notation

How does abstract index notation work? What do the the indices represent? I know the Lorentz transformation tensor in arbitrary direction, so if you want to use a specific tensor in an example, that would be a good one.
18. ### Rocketship problem- fuel burn and gravity

Consider a spaceship, initially at rest on the surface of a planet that has no atmosphere. It takes off with constant force from thrust. The fuel mass decreases linearly with time, and the rocket accelerates directly away from the planet (no curving off orbit the planet). Use GMm/r^2 for...