The four fundamental fundamental equations of electromagnetism.

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Is there any correlation between mass-energy equivalence and Maxwell's 4th equation?

I wonder, how came in both equations proportionality constant is exactly $c^2$? $$c^2(\nabla \times B) = \partial E/\partial t$$ where $E$ - electric field $$c^2m = E$$ where $E$ - energy I am ...
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1answer
216 views

Electric field from current without Maxwell's law of induction

A long, straight wire carries a current that decreases linearly with time. What is the direction of the induced electric field outside the wire? I would interpret this as follows: a current ...
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1answer
136 views

Surely force on shell can't be balanced by field momentum?

Imagine a particle with charge $q$ at rest at the origin. It is surrounded by a concentric spherical insulating shell, also at rest, with charge $Q$ and radius $R$. At time $t=0$ I apply a constant ...
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1answer
385 views

Proof of equality of the integral and differential form of Maxwell's equation

Just curious, can anyone show how the integral and differential form of Maxwell's equation is equivalent? (While it is conceptually obvious, I am thinking rigorous mathematical proof may be useful in ...
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129 views

Reaction-at-a-distance: Do charged plates immediately repel each other?

Imagine that we have a pair of parallel plates, $A$ and $B$, separated by some distance as in Fig. $1$ above. At time $t_1$ we simultaneously charge both the plates. This could be done by ...
2
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66 views

How to properly construct the electromagnetic tensor in curved space-time? (Part II)

In this question, I am testing what was previously discussed. I can't seem to get my results to match D'Inverno's electromagnetic tensor for a charged point (page 239 of his book - Introducing ...
2
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65 views

One question about derivation of Maxwell equations

I saw the following way of derivation of Maxwell equations: author starts from Lorentz transformations for the 3-vector of force, then he applies them for the Coulomb law, after that gets the Lorentz ...
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143 views

Maxwell equations and symmetry

Do the full inhomogeneous Maxwell equations obey parity (P) and time reversal (T) symmetry separately or only the full CPT symmetry? I believe the homogeneous Maxwell equations obey parity and time ...
2
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279 views

Electromagnetic duality

A key aspect of modern physics is the mapping of theories or different descriptions of a theory into a one-to-one correspondence. As I am trying to further understand the electromagnetic field tensor, ...
2
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0answers
92 views

Two spinor tensors and Maxwell's equations

Let's have two symmetric (by the indices) spinor tensors $F_{ab}, F_{\dot {a}\dot {b}}$ and conditions $$ F_{ab}, \partial^{\dot {a} a}F_{ab} = 0, \quad F_{\dot {a}\dot {b}}, \partial^{\dot ...
2
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0answers
144 views

Electromagnetic inertia due to advanced radiation?

The scalar potential $\phi$ and vector potential $A$ at a distance $r$ from a charge $q$ are given approximately by $$\phi = \frac{q}{r}$$ $$\mathbf{A} = \frac{q\mathbf v}{r}$$ where the constants ...
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0answers
45 views

Were Maxwell's equations first formulated by McCullough?

Some years ago, I heard a talk about a an Irish or Scottish physicist named McCullough who had formulated Maxwell's equations several years before Maxwell. This fellow was recognized for his work, ...
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110 views

Sommerfeld radiation conditions for an electromagnetic field

There is some confusion in the definition of Sommerfeld radiation conditions for an electromagnetic field, which are related to the asymptotic behaviour of the field for a distance $r \to \infty$ ...
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0answers
113 views

Electromagnetism - Proof of the Uniqueness theorem for an external problem

In the electromagnetic Uniqueness theorem, we consider a volume $V$ enclosed by a surface $S$. It is initially assumed that two different fields are valid solutions for the Maxwell's equations with ...
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0answers
47 views

Do these steps demonstrate that acceleration of charged particle is proportional to current?

One formulation of Maxwell's Gauss Law for electric field is: $$\bigtriangledown E = 4 \pi k \rho $$ This can be worked into the Divergence Theorem as follows: $$\int\int_{A} F_\perp \:dA= 4\pi k ...
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60 views

Maximise magnetic force at one point while minimizing at another

Is it possible to have a magnet that attracts one object strongly, but not another object behind that first object? Given an (electro-) magnet M above two thin parallel steel sheets P1 and P2 in the ...
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0answers
94 views

Can universe be a closed manifold?

I had a question at MSE which gave a rise to another question. Maxwell equations can be written in form $$d\star F = J$$ Then by Stokes theorem we have $$ \int_U J = \int_U d \star F = ...
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28 views

Jacobian of a transformation on Maxwell equations in cylindrical coordinates

In an area called transformation optics, they transform Maxwell equations from one space coordinate system to another, and then using the fact that Maxwell equations retain the same format under ...
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32 views

Poynting Vector between Capacitor - With electrons in between!

Consider a capacitor with voltage $V = V_0 cos(\omega t)$, radius $a$ and separation $d$. Electrons are distributed uniformly with number density $n$. I want to find the poynting vector between the ...
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81 views

Obtain the same Maxwell's equation after a change of coordinates

In the usual $(x,y,z)$ system of coordinates, if we expand the Maxwell's curls equations for phasors $$\nabla \times \mathbf{E} = - \mathbf{J}_m - j \omega \mu \mathbf{H}$$ $$\nabla \times \mathbf{H} ...
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40 views

E and B field from Time Varying Current

How would I go about calculating the B field and E field from a time varying current charging a capacitor. Theoretically I feel like a solution should exist, but there seems to be a dependence between ...
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68 views

Compatibility between solutions of explicit Maxwell equations vs. wave equation?

When trying to solve for the allowed propagation frequencies in a cylindrical waveguide, I approached the problem by solving the wave equation for all three components of $\bar{E}$, and subsequently ...
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49 views

Deduce magnetic field based on electric field

I'm learning Maxwell's electromagnetic equations and i can't wrap my head around this problem: Given the volume $x\in [0,1], y\in [0,1], z\in [0,1]$, electric field $\vec E(x,y,z,t)$ and material ...
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68 views

How to do this index notation differentiation?

I am studying classical Maxwell fields and I am stuck on this differentiating part. How can I derive the result given below ? $$\dfrac{\partial}{\partial(\partial A_{\mu}/\partial x_{\nu})} ...
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54 views

Measurement of speed of static electric field propagation?

Could one measure the time delay between charging up an electrode and measuring the static electric field at some distance? For example I've looked up the specifications of an Electric Field Meter ...
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58 views

One more time about the connection of Weyl tensor and gravitational waves

There is differential identity with Weyl tensor and energy-momentum tensor: $$ D^{\lambda}C_{\lambda \alpha \sigma \beta} = 4 \pi G \left(D_{\sigma}T_{\alpha \beta} - D_{\beta}T_{\alpha \sigma} + ...
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118 views

Solving the source free Maxwell equations for plane waves

I've been trying to solve the maxwell equations: $$\nabla\cdot\vec{D}=0,\quad \nabla\cdot\vec{B}=0$$ $$\nabla\times\vec{E}=-\frac{\partial \vec{B}}{\partial t},\quad \nabla\times\vec{H}=\frac{\partial ...
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486 views

Faraday law, third Maxwell's equation in Mathematica

Three question about this equation: $ \displaystyle\nabla\times\mathbf{E}=-\frac{\partial \mathbf{B}}{\partial t} $ 1 If I solve this equation with Mathematica, I find the magnetic field ...