Questions tagged [maxwell-equations]

A set of four equations that define electrodynamics. They comprise the Gauss laws for the electric and magnetic fields, the Faraday law, and the Ampère law. Together, these equations uniquely determine the electric and magnetic fields of a physical system. Do not use this tag for the thermodynamical equations known as Maxwell's relations.

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Why are electric monopoles not interpreted as topological defects but magnetic monopoles are?

What explains this asymmetry between the electric and magnetic fields if both electric and magnetic monopoles exist? Can't Maxwell's equations be formulated to be symmetric between the two in the ...
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Why does a steady electric current imply a time-independent magnetic field?

From No-Nonsense Electrodynamics, pg. 95: I understand that if $\partial_t \rho = 0$, then the resulting electric field configuration is time-independent, since Gauss's law for the electric field ...
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Electromagnetic field incident on a surface that absorbs the entire electric field

I am trying to solve a question that is phrased: "An electromagnetic wave is incident on a surface which absorbs all the electric field. Use Maxwell’s equations to determine the magnetic field on ...
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Simultaneous Lorentz and Galilean invariance

The introduction of the Lorentz transformation is usually motivated by the Galilean failure when it comes to Maxwell's equations. Are there physical systems that exhibit both Lorentz and Galileo ...
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Solution of electric and magnetic fields wave equations in free space

While solving for the electric and magnetic wave components using Maxwell's equations in the free space, I have read that it was assumed that propagation of the wave is in z direction and that all the ...
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Charge $q$ near Current-Carrying Wire

A charge $q$ nears a current-carrying wire. How does $q$ move? Specifically, what is $\vec{r}(t)$ for $q$? I've found the direction of some of the forces acting on the charge $q$: Using the Biot-...
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Electric and magnetic fields boundary conditions

For a perfectly conducting and perfectly dielectric interface, I understood that tangential component of electric field is zero and continuous. But I have read that the normal component of magnetic ...
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Motion of Test Charge in EM Field [closed]

I have a negative infinite sheet of charge moving at a velocity $v$ in the $+x$ direction. A test charge $Q$ with mass $m$ moves at a constant velocity $v$. My Question is simple: How will the test ...
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Movement of Particle in Electromagnetic Field

I'm a high schooler who just finished learning Maxwell's Equations. I'm trying to visualize the movement of a charged particle in a field. I have an infinite sheet of positive charge oriented on the ...
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How to test the solution for the magnetic field around a wire

One can arrive at the equation for the magnetic field around an infinite wire in several ways(biot savart law, I used the integral form of Ampere's law). The solution is well known and of the form $$ ...
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Electromagnetic waves from current carrying wires [closed]

Consider a current-carrying wire. In the first case, the current in the wire is increasing with time. Since the magnetic field is changing, EM waves will be produced. My question is what will be the ...
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Thus it is proved that there is no such a thing as magnetism [duplicate]

I saw a proof that shows that there is no such a thing as magnetism. I think the fault in the proof is with simply connected regions. Proof is as follows: One of Maxwell’s equations tell us that $$\...
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Phase reversal of light using polarizer

I have 5 polarizers in series. The first polarizer is vertical. The second polarizer makes an angle of 45 degrees from the first polarizer in a clockwise sense. The third polarizer makes an angle of ...
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Intuitive explanation of Maxwell Ampere Equation (my take) [closed]

I was trying to find some intuitive explanation of the Maxwell's 4th Equation, so I tried it myself.. not sure if it holds.. Asking for better explanations
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What would Maxwell's equations look like in a universe which followed Galilean transformations?

I was wondering how the electromagnetic force would behave in a Gallilean transformation universe. Would the magnetic force be non-existent? We know that Gallilean transformations are Lorentz ...
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Artificial Muscle | Is Electromagnetic Attraction Better then Maxwell Stress?

I was watching a TED-talk on artificial muscle, HASEL, where the inventor demos that an insulated oil in the presence of electric potential field gets displaced due to induced Maxwell stress. In other ...
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Electromagnetic wave equation in exponential refractive index

I’m trying to find the electromagnetic field of an electromagnetic wave in an exponential refractive index. What that means is the refractive index has the form $n\left(y\right)=e^{sy}$. I know for a ...
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Doubt in a property of Laplace equation

One of the Laplace equation's property says that the maxima and minima can only occur at the boundaries. Okay so lets take 2 positive charges, one at the origin and the other $d$ distance apart on the ...
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1answer
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Where is electromagnetic induction in the Jefimenko equations?

I'm currently exploring the Jefimenko Equations and practicing using them to find things like the electric field from a particle or the magnetic field around a current. In general, I've read that the ...
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Is general and special relatively a consequence of Maxwells equations?

It seems, more or less that, special relativity simply states the effect on space and time assuming that Maxwell's equations hold true everywhere, and general relativity... ...well I was thinking it ...
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Why do we say electromagnetic waves are self-propagating if they follow an inverse square law?

Electromagnetic waves are frequently described as "self-propagating", implying a mode of propagation distinct from that of electrostatic fields; but as I understand things, both have ...
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Why can the induced magnetic field be ignored in this problem?

I am given the following conducting track, where on its right side there is a conducting rod with mass $m$ and length $a$ which is free to slide on it. There is a constant magnetic field throughout ...
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Cauchy problem of classical Maxwell equations in Minkowski spacetime

I'm wondering a bit about the classical Maxwell equations in flat spacetime and their Cauchy problem. For the following, I suppose that the sources are already given and don't react to their own ...
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4answers
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Why is Maxwell's equations correct and not Newton's laws of motion?

In many books, while introducing Special relativity it is shown that Maxwell's equations are not consistent with Galilean transformations.So either Galilean transformations(and consequently Newton's ...
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Finding the magnetic field by using Maxwell's laws (differential form)

According to my physics book, one can use the following laws to identity the magnetic field: div B = 0 rot B = μ0J My book also states that, given a specific current density vector, many magnetic ...
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Is this a possible derivation of the electromagnetic wave equation?

Some Background: I've been trying to understand electromagnetic waves, how they travel, and how they're produced. After some Googling and Wikipedia(ing?) I've learned that we use the EM Wave Equations ...
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What exactly is enclosed current?

In the realm of magnetostatics, consider the integral form of Ampere's law: $$ \oint_C \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{enclosed}$$ What I realized is when asked the question "what is the ...
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Voltage across rod in time varying magnetic field

If a slim conductor of some length $l$ and diameter $d\ll l$ is placed in a magnetic field $B$, and the field is changed by $\frac {dB}{dt}$, what (if any) is the voltage $V$ induced across the ends ...
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Can Maxwell's equations be generalized to all fields?

For having studied both classical and quantum optics, I regard Maxwell's equations as the grand "cheat sheet" from which (almost) all optical/photonic phenomena can be derived. Yet, I also ...
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Does Maxwell stress tensor take into account dielectrophoretic and electrophoretic forces?

I'm a mechanical engineer (this question might be very fundamental), and I am working on simulating the behavior of a particle in water when subjected to an electric field. In my simulation, I am ...
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1answer
68 views

Understanding why $\frac{\partial (F_{\mu \nu} F^{\mu \nu})}{\partial (\partial_\lambda A_\beta)}=4 F^{\lambda \beta}$ in Maxwell's Equations [duplicate]

In trying to derive Maxwell's equations from $$S=\int d^4 x\left(-\frac 1 4 F_{\mu \nu}F^{\mu \nu}\right)$$ Where $$F_{\mu \nu}=\partial_\mu A_\nu-\partial_\nu A_\mu$$ I'm trying to show that $$\frac{\...
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Do Maxwell's Equations depend upon an orientation of space?

Even when we cast Maxwell's Equations in as coordinate-independent form as possible, $dF=0$ and $d \star F = J$, we still have to make use of the Hodge star $\star$ which is defined relative to an ...
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Specific note that is not clear for me in and the derivation of maxwell equation $\oint \vec{B} \cdot d \vec{r}=\mu_{0} I_{e n c}$

I know this is not the full equation but right now in this path of the course that what we learned so far. We studied that a wire along the $z$ axis produces magnetic field $\vec{B}=\frac{\mu_{0} I}{2 ...
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A question about Maxwell's Equations

These notes on Electromagnetism (chapter 3.1.2, section "A Solenoid") say the following: We solve Ampère's law in differential form. Anywhere other than the surface of the solenoid, we have ...
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What does mutual induction of electric and magnetic fields in an EM wave mean?

Changes in the electric field makes changes in magnetic field and vice versa. What does this logically mean? It looks like an infinite loop. I don't understand how this helps the EM wave propagate. I ...
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Reflection and refraction by moving charge: can method of images be used?

Suppose we have a point charge moving inside the halfspace $z>0$ with a given trajectory $r(t)$. Assume that $z>0$ halfspace is Vacuum and the $z<0$ halfspace is glass or some linear ...
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1answer
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Electromagnetic Potential in Relativity

Studying Special Relativity we discover that Maxwell's Equations can be also written in the following way: $$\partial _\mu F^{\mu\nu}=\mu_0J^\nu$$ $$dF=0$$ Where: $F$ is the Electromagnetic Tensor, $J$...
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Conservation of charge in Maxwell's equations

In Zangwill's second chapter (on Maxwell's equations), problem 2.4 states the following- "The magnetostatic equation $\nabla \times \textbf{B} = \mu_0\textbf{j}$ is not consistent with ...
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Is it possible to derive the Maxwell equations directly from the Electromagnetic tensor?

The Lagrangian for ED without Gauge fixing term is given by $$\mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu},\quad \text{where}\quad F_{\mu\nu}:=\partial_\mu A_\nu-\partial_\nu A_\mu.$$ I was wondering ...
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How does the existence of a monopole affect the magnetic vector potential in gauss's law for magnetism? [duplicate]

Gauss's Law for magnetism is $$ \nabla \cdot B = 0 $$ This allows us to write the magentic field $B$ as the curl of another field the $\textbf{magnetic vector potential, } A$. $$ B=\nabla \times A $$ ...
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Is Maxwell's theory of electromagnetism completely validated? [duplicate]

Most of the time, I read articles or watch videos saying that Hertz experiments validated Maxwell's theory of electromagnetism. But Hertz only confirmed the existence of waves (that are perhaps ...
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In wave equation, what is the meaning of poynting vector, compare to the amplitude vector?

I'm looking at this equation: $$\tilde{\vec E}(\vec r,t)=\tilde{\vec E}_0e^{i(\vec k\cdot r-\omega t)}\hat n \tag{1}$$ I thought that $\tilde{\vec E}_0$ was the polarization vector, but then he added $...
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Do Maxwell's equations contain any information on the time evolution of the current density $J$?

The answers to Can the Lorentz force expression be derived from Maxwell's equations? make clear that Maxwell's equations contain only information on the evolution of the fields, and not their effects ...
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Photoelectric effect: Beginning of the complexities [duplicate]

We are taught that in photoelectric effect if the frequency of light is lower than the threshold, then no matter how long a metal is exposed to it there won't be any ejection of electrons. This made ...
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Why would the two areas not shrinking together cause the total charge to become infinite?

I am currently studying Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edition, by Max Born and Emil Wolf. Chapter 1.1.3 Boundary conditions at ...
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Why visible light satisfies Maxwell equations? [duplicate]

As it is described in standard textbooks I looked at, the Maxwell equations were first established for electromagnetic fields created by electric currents. Then it is stated that it was discovered ...
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Magnetic induction by changing permeability of a uniform magnetic field?

As far as I know, magnetic fields are created by either magnet or running current, which both can be changed by changing the permeability of the medium and thus change the magnetic flux through the ...
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1answer
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How to remember Maxwell equation in Gaussian units? [closed]

I know Maxwell relation in MKS unit $$\begin{cases}\nabla\times E=-\frac{\partial B}{\partial t},\\ \nabla \times B = \mu_0 \epsilon_0 \frac{\partial E}{\partial t} + \mu_0J,\\ \nabla\cdot E = \frac{\...
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Maxwell Equation: Definition of Invariance

Knowing Lorentz Transformation and knowing the differential formulation of Maxwell Equations: Precisely, what is the meaning of the statement: "Maxwell equation are invariant under Lorentz ...
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When all does Ampere's circuital law FAIL to work? What are the inconsistencies that arise when considering conducting wires of finite length?

Does Ampere's law hold when trying to compute the line integral around a closed-loop; if the current-carrying wire is of finite length? It is obvious that the integral values change with changing the ...

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