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    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...
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    Maxwell's equation and Helmholtz's Theorem

    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?
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    Maxwell's equation and Helmholtz's Theorem

    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...
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    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...
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    Help with Newtonian Potentials for Helmholtz Decomposition

    See the thread in the classical physics forum. I started this one because no one was responding to the other one.
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    Newtonian potential in Helmholtz decomposition

    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...
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    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...
  8. S

    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...
  9. S

    Solving Differential Equations Involving Vector Fields

    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)
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    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.
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    Operator questions

    How did you get the symbols to work?
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    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?
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    Curl reversibility?

    I'm not sure what I was thinking there, haven't been getting alot of sleep lately.
  14. S

    Optics - why chromatic aberrations

    Reflecting telescopes (as opposed to reflecting) have no chromatic aberration. I find it surprising that there are no reflecting cameras
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    Curl reversibility?

    I think I know how I can do this. Is it possible for a vector field to be perpendicular to its divergence at a point?
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    Curl reversibility?

    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...
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    Curl reversibility?

    k-Space was mentioned, and I found that k-space requires tensors
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    Curl reversibility?

    Is there any good way to do this that doesn't involve tensors?
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    Curl reversibility?

    Is it because the current is not constant?
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    Curl and vector fields

    Where can I find this? I'm a high school student learning outside the classroom, so I don't have access to any resources that require subscription
  21. S

    Curl reversibility?

    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
  22. S

    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
  23. S

    Is fire life?

    Actually you could in principal make a new rabbit if you worked fast
  24. S

    Curl reversibility?

    Should I be asking the differential equations section?
  25. S

    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?
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    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...
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    Fresnel Equations Question

    I hadn't, as not all formalisms involve matrices (as far as I know)
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    Fresnel Equations Question

    nothing
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    Fresnel Equations Question

    Could I get a link to this Jones Formalism?
  30. S

    Fresnel Equations Question

    Is there a generalized Fresnel equation for the reflection of light with arbitrary polarization (between p and s)?
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