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...
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...
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...
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...
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.
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?
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
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?
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...
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?
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?
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...
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.
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...