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...
Actually you can, but it is not a continuous current. Charge density = charge / r^3.
Besides, the Biot-Savart law requires a continuous current.
My question remains unanswered. How can I set up my integration to work around the singularities?
current is charge density times the velocity of the generating particle, so there is current. The electric field is changing in the reference frame I am using, which also generates magnetic field.
I do not have limits of integration because I do not know how to set up the limits of...
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 am aware of the limitations of learning advanced materials on the internet. However, until I start college next year, it is my only option.
The reason the negative exponent bothered me is because (I thought) it would mean that the final field is increasing as distance increases, which...
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...
The application here is maxwell's equations. However, my use of point particles precludes the Biot-Savart Law (as the current density is constantly changing)
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?
How would one find the equation based on its divergence?
The divergence is this case is the partial derivative with respect to time of the divergence of the time-varying electric field. So basically what is happening is you take the divergence of the electric field, take the partial...
In this case, the magnetic field is being created by an electric dipole consisting of two point particles of equal mass and opposite charge in mutual orbit, not a current, so the Biot-Savart law doesn't apply
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...