# Tagged Questions

The four fundamental fundamental equations of electromagnetism.

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### Justification of Physical Laws [on hold]

I'm a maths student, and I've studied quite a lot of mathematical physics. All my courses have a similar style - we state the laws of the system, and then deduce the physical consequences as theorems. ...
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### Is it true that $\frac{d}{dt}\int_S \mathbf{B} \cdot d \mathbf{a}$ goes to zero if the amperian loop delimiting $S$ contracts indefinitely?

I suppose to have an ordinary magnetic field: in the answer I'm not interested to involve Dirac delta: the integral goes to zero. I want to focus on another point: an infinitesimal physical quantity ...
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### About the closed line integral of electric field intensity

In electrostatics, we know that the closed line integral of electric field is zero : \oint\limits_{C} \mathbf{E}\left(\mathbf{x}\right) \boldsymbol{\cdot} \mathrm{d}\mathbf{x}=\;\;...
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### Why does current follow a conductor above a ground plane

Suppose there is a conductor above a ground plane. Current flows from a source through the conductor to a load on the other side. Depending on the frequency of the current the return path through the ...
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### How do charges accumulate even though current flows through a capacitor?

I don't understand why do charge accumulate on each plate of capacitor.I learned about displacement current which flows through the gap of the capacitor and this makes the circuit continuous.But why ...
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### DC current in a wire

I'm sure that this question was addressed here before, but I failed to find any other instances, so with your permission I ask the question myself. I'm experiencing a very disturbing glitch, there is ...
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### Does Maxwells equations imply $R=const*\rho$?

Suppose we have a resistor in a strange shape, filled with a medium of resistivity $\rho$, assuming only maxwells equations apply, is it true that R is proportional to rho, even for very low ...
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### Defining electromagnetic stress tensor for non-linear media

In textbooks, the electromagnetic stress tensor (in vacuum also called Maxwell stress tensor) is usually derived for linear media, implying that $$\vec D = \epsilon_0 \epsilon_r \vec E$$ My question ...
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### Deriving an equation in Maxwell's “a treatise on electricity and magnetism” [duplicate]

I am reading Maxwell's "a treatise on electricity and magnetism" and I need a derivation of formula 16 $\left(M=\iint\dfrac{\cos\varepsilon}{r}\mathrm ds~\mathrm ds'\right)$ (in the page below) using ...
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### Confusion in Maxwell's derivation of Ampere's Force Law - Part II [closed]

I am reading Maxwell's "a treatise on electricity and magnetism, Volume 2, page 156" about "Ampere's Force Law". I have some confusion in the following pages: My question is of two parts: 1. ...
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### Rewriting Maxwell's equation in tensor form [closed]

Suppose $F_{ij}=\epsilon_{ijk}B_k$, how to prove the following: $\partial_iB_i=0$ becomes $\partial_iF_{jk}+\partial_jF_{ki}+\partial_kF_{ij}=0$ $B_iB_i$ becomes $F_{ij}F_{ij}/2$ I can see that ...
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### How would you define electrostatics and magnetostatics starting from Maxwell's equations?

I'm reading Griffith's text, and he starts by defining Electrostatics as requiring the source charges don't move. I've seen a few slightly different definitions of electrostatics and magnetostatics. ...
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### What is the physical meaning of a magnetic conduction current?

In electrodynamics, it is possible to have an electric conduction current, whereby $J=\sigma_e E$, with $J$ being the current, $\sigma_e$ the electrical conductivity and $E$ the electric field (this ...
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### Why do we use gauges in Maxwell equation?

While solving the Maxwell's equation we often use the Lorenz or Coulomb gauge, but why is that? Are the equations unsolvable if the gauge is not fixed? Or is it just for the simplicity?
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### What are the differences between the differential and integral forms of (e.g. Maxwell's) equations?

I would like to understand what has to be differential and integral form of the same function, for example the famous equations of James Clerk Maxwell: How to know where to apply each way? Excuse ...
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### Tensor notation of Maxwell's equations

Tensor notation of Maxwell's equation read So when we explicitly try to find the Maxwell's equation from the above tensor equation we only get gauss law and curl of B. The div.B=0 and curl of E are ...