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    I Expressing the magnetic vector potential in terms of its curl

    We have the retarded magnetic vector potential ##\mathbf{A}(\mathbf{r},t) = \dfrac{\mu_0}{4\pi} \int \dfrac{\mathbf{J}(\mathbf{r}',t_r)}{|\mathbf{r}-\mathbf{r}'|} \mathrm{d}^3 \mathbf{r}'## And its curl ##\mathbf{B}(\mathbf{r}, t) = \frac{\mu_0}{4 \pi} \int \left[\frac{\mathbf{J}(\mathbf{r}'...
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    I Instantaneous solutions to Maxwell's equations' potentials conversion?

    This page shows solutions for Maxwell's equations of the electric and magnetic potentials (Eqn.s (509) and (510)): They are derived with the aid of a Green's function:
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    I Proving radial properties of particular dimensionless surface plots?

    We have a surface function z = f(x,y) ; f(x,y) only contains dimensionless constants, and is itself dimensionless. If we convert it to cylindrical co-ordinates, z = f(r,θ) , does z only depend on θ? Meaning we can remove r from the equation, literally.
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    I Looking for more accurate energy-momentum transformations for photons

    Photons deviate from the above energy-momentum transformations under certain circumstances while still in flat space-time, I'm wondering what set of transformations would more accurately describe them over as wide a range of circumstances as possible, still in flat space-time, I've searched and...
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    I Do binoculars change the distance which the eyeball focuses?

    When you look at an object, say, for example, 30 feet away, your eyeballs adapt to focus at that distance of 30 feet. When you look at the same object through a pair of binoculars, at what distance do your eyeballs adapt to focus at? Is it more or less than 30 feet? This is not a question...
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    I Relativistic form of the displacement current using the Biot-Savart Law

    The Biot-Savart law which describes a magnetic field created by a displacement current: $$\frac{dB}{dV}=\frac{\mu_0\epsilon_0}{4\pi}\frac{\frac{∂E}{∂t}×r}{r^2}$$ What's the relativistically co-variant form of this equation? Is the introduction of speed of light propagation delays enough, or...
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    I Magnetic Field of a Moving Charge and the Displacement Current

    We all know a moving charge generates a magnetic field. A moving charge also generates a displacement current ∂E/∂t. Is the magnetic field generated entirely due to the presence of the displacement current, or is there an independent, separate effect which contributes to the magnetic field?
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    Attempt at volume integration to compute the full field equation

    I'm trying to figure out this volume integral, a triple integral, of a 9-variable function. 3 Cartesian-dimension variables, and 6 primed and un-primed co-ordinates. After the volume integration, the un-primed co-ordinates will have been gotten rid of, leaving a field function in terms of...
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    I What's the derivation in a moving magnet & conductor problem?

    In the Wikipedia page of the moving magnet and conductor problem, it asserts "This results in: E' = v x B", but does not elaborate why. What's the full derivation?
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    I What's the amount of energy lost in Total Internal Reflection?

    In Total Internal Reflection, the beam can still lose some energy as it reflects off the boundary of the medium it is within. This isn't covered under the Fresnel equations. The energy loss is probably lost in the form of evanescent waves. I tried searching for the formulae describing the...
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    I Maximum Amplitude of Sound Wave?

    This animation demonstrates a longitudinal wave by means of moving bars. I realized that if we increase the amplitude of the wave, the bars will eventually start passing through each other, which sounds (no pun intended) like an unphysical scenario. Does this mean that there is a cap, a...
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    I Energy Loss During Total Internal Reflection

    When a laser beam reflects during total internal reflection, how much of its intensity is lost? I can't the use Fresnel equations as this is for total internal reflection. If you don't know the answer to the above question, what about the same question, but for mirrors instead? What are the...
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    Can we get Higher Frequencies from an Oven Magnetron?

    Is it possible, and if so, how should we modify a typical oven magnetron so as to produce higher frequencies of EM radiation?
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    I Is it Impossible for Entanglement > FTL Communication?

    Lots of people have wondered about whether we can get FTL communication from entanglement. My question is slightly different. Is it impossible to get FTL communication out of entanglement? If it has been shown to be impossible, then we can shut off the entanglement-FTL avenue altogether and...
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    I Function as a Solution to Specific Conditions

    I'm trying to solve some statistical mechanics. This problem appeared. ##\frac{f\left(0\right)}{f\left(a\right)}f\left(x+a\right)=f\left(x\right)## Any idea as to which function will satisfy this equation?
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    I Applicability of E and B field Transformations

    I have a question regarding these transformation formulas: ##\begin{align} & E'_x = E_x & \qquad & B'_x = B_x \\ & E'_y = \gamma \left( E_y - v B_z \right) & & B'_y = \gamma \left( B_y + \frac{v}{c^2} E_z \right) \\ & E'_z = \gamma \left( E_z + v B_y \right) & & B'_z = \gamma \left( B_z -...
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    Best Way to measure Relativistic Rocket Acceleration?

    Someday, mankind will be able to construct rockets that can move at relativistic speeds. The acceleration is given by ##a=\frac{F_0}{γ^3m_0}## ##F_0## can be easily measured by placing a force gauge on the rocket itself. The acceleration is much harder to measure, is has to be measured in a...
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    I How was Kramer's Law derived?

    Kramer's Law describes the spectrum of Bremsstrahlung radiation: How did Kramer derive this formula?
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    I For Dummies Derivation of Radiation Pressure>Energy Density?

    The formula for the radiation pressure P in n-dimensional space for a given internal energy density u is ##\frac{u}{n}##. I would really appreciate it if someone could provide a link that gives a simple derivation of this formula for dummies like me.
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    I Breakdown of Planck's Law under certain Conditions

    The difference between Planck's Law and the Rayleigh-Jeans' Law is, in Rayleigh Jeans, the average energy per mode is ##kT##, whereas in Planck, it is ##\frac{hc}{λ(e^\frac{hc}{λkT}-1)}##. These average energy formulas are multiplied by another formula to give either Planck's Law or the...
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    I SR Doppler Effect: Differences in Wave VS Momentum Models

    In his seminal paper on Special Relativity: On the Electrodynamics of Moving Bodies, Einstein derives a formula for the Relativistic Doppler effect. See this section: § 7. Theory of Doppler's Principle and of Aberration The formula is: In this Wiki article, the same formula is derived. The...
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    I How are Vectors described in Bispherical Coordinates?

    I was reading a paper that described a vector field in terms of its three components , ##A_σ,A_τ,A_φ##. with σ, τ and φ being the three bispherical coordinates. what does ##A_σ## mean? In what direction does the component point? Likewise for the other two components.
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    I Field Lines of an Electric Dipole?

    It isn't difficult to find the electric field of a dipole. However, it is tricky to find the field lines. All points of a field line have to be parallel to the electric field at those points. A tangent, which is the derivative, is parallel. We can hence formulate the equation for a field line...
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    I Electric Field Between Two Metal Balls.

    Imagine you have two identical metal balls, each carrying the same amount of charge, but with one ball being positive and the other negative. When you bring them close together, there will be polarization, so you can no longer treat the balls as point charges. How does one find the charge...
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    I Lorenz Curves and Distributions...

    Is it correct to say that the Lorenz curve is the normalized integral of the quantile function with respect to the x-axis?
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    I Inverse of Maxwell-Boltzmann Distribution and Planck's Law?

    I'm looking for the inverse functions of the Maxwell-Boltzmann distribution and Planck's Law. Planck's Law in terms of the wavelength. Any of you know of any literature on this topic?
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    I Help me Integrate this function

    I would like to integrate w.r.t. x, the rest are constants. This is not homework; it is related to a physics problem regarding single-slit diffraction.
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    I Does a Magnetic Moment μ exist for any closed current loop?

    I'm asking the above question as I imagined a current loop made out of a curving wire that cannot fit into a flat plane. Where does the direction of μ point then? Also, is there only one μ value for any current loop, independent of the chosen axis of tilting? Or can a current loop have...
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    I Finding the Electric Field of a Hollow Cylindrical Conductor

    I am trying to find the electric field of a hollow, open-ended, thin-walled cylindrical conductor. I am trying to solve something regarding LINACs: Assume we have an isolated, hollow, open-ended, thin-walled cylindrical conductor, with a net charge. The net electric field within the...
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    I Zero-Divergence of Rate of Change of Magnetic Flux

    Let's introduce a time-varying scalar field ρ(x,y,z,t) [charge density] and vector field J(x,y,z,t) [current density] Assuming the system follows Maxwell's equations, what must both fields satisfy such that ##∇⋅(\frac{∂B}{∂t})=0## ?