Questions tagged [classical-electrodynamics]

Classical electrodynamics is the discipline that studies electromagnetic phenomena – such as electric and magnetic fields, radiation, and the dynamics of charged bodies – in classical terms.

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Microscopic explanation for Hooke’s law

This figure shows the force between two atoms - at separation d there is no repulsive or attractive force, but for separation between d and the minimum, there is an approximately linear increase ...
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What is the force corresponding to Lamor's formula for EM radiated power?

The rate at which electromagnetic energy is radiated is given by Lamor's formula. What is the corresponding rate at which momentum is radiated and hence force to this?
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The issues when thinking about the magnetic flux law as being universal in modeling

$$ \varepsilon = -\frac{\partial \Phi}{\partial t} =-\frac{\partial (BA)}{\partial t} $$ Any instance of considering the emf induced in a system, I usually think of the flux law first, I intensely ...
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What are the electric and magnetic fields of an arbitrarily moving point charge assuming instantaneous field propagation for simplicity? [closed]

I could find an equation for the magnetic field. It is called the Biot-Savart law: $$ {\vec{\pmb{B}}} = \frac{\mu_0}{4\pi} \cdot q \cdot \frac{1}{r^2} \cdot \left( {\vec{\pmb{v}}} \times {\hat{\pmb{r}}...
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Repulsive force from charge accumulation in a capacitor plate?

During a charged state of a capacitor (Regardless of the type of capacitor), Simple parallel plate: .png Parallel plate with dielectric material in the gap: ]3 Supercapacitor: How is the ...
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Why is it that magnetic fields(or any field)not move in space? [closed]

When I imagine a magnetic field produced by a magnet, or the electric field produced by a charge, I've learned that the fields are stationary, however, their value(across space) changes. If I placed ...
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111 views

What does Maxwell's equations predict for the propagation of EM waves converging to a point?

Maxwell's equations model EM radiation as propagating away from an accelerating charge. Suppose instead the propagation of this EM radiation is reversed and presented as a source-free boundary ...
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Electromotive force in the presence of non-steady currents

Griffiths's Introduction to Electrodynamics states $$\mathcal E = \oint \mathbf f \cdot d\mathbf l$$ In which $$\mathbf f = \mathbf f_s + \mathbf E$$ Where Griffiths describes the summation as ...
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Using the Lorentz force equation twice to model to different phenomena?

In a rail system, can I apply Lorentz force separately to: Derive the work required to move the charges(motion of current); Derive the kinematics relative to the rod's motion; All stemming from: $$ ...
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In electrodynamics, why do we say $\mathbf J = \sigma \mathbf E$ and not $\mathbf J = \sigma (\mathbf E + \mathbf v \times \mathbf B)$?

Griffiths notes it's because charges have an extremely low $\mathbf v$, so it's essentially an approximation, but aren't charges meant to be electrons? How can they be moving slowly? I usually think ...
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Relationship between the: Power supply's electric force for current flow, and Lorentz force equation for electric force?

$$ F = qE + qv \times B$$ For the Lorentz force relevant to a current carrying wire, that is caused by the motion of a wire w.r.t to an exterior magnetic field $B$, the second term($qv \times B$) on ...
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Displacement currents, aren't really currents?

I'm confused with this definition of displacement currents within capacitors via Wikipedia: However it is not an electric current of moving charges, but a time-varying electric field. It's a ...
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Energy-momentum tensor of the electromagnetic field

I have to derive the electromagnetic energy-momentum tensor from Noether's theorem and translation invariance. Due to translation invariance and gauge transformation: $$\delta A_\mu= a^\nu F_{\mu\nu}$$...
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Griffiths Electrodynamics Problem 9.39: How can $\sin(\theta_T)$ be greater than one?

When an electromagnetic wave strikes an interface between two linear media, Snell's law states that $\frac{\sin(\theta_T)}{\cos(\theta_I)} = \frac{n_1}{n_2}$ where $\theta_I$ is the angle of incidence,...
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Diffraction by induced quadrupoles

This is a very interesting problem that I've been struggling to solve for a week, so I decided to ask for some orientation, as I think it could also be of interest for the community. Let's consider a ...
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71 views

Invariance of Maxwell action

I have to show that the Maxwell action $$S=-\frac{1}{4}\int d^4x F^{\mu\nu}F_{\mu\nu}\,$$ is invariant under translation: $\delta_aA_\mu=a^\nu \partial_\nu A^\mu$ with $a^\mu$ as arbitrary and ...
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How do we know that electric charges are invariant?

According to tparker at Why charge is Lorentz invariant but relativistic mass is not? So there are two different ways to generalize the mathematical form of Coulomb's law to make it ...
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Subarea within a changing magnetic flux?

If I were to introduce a boundary area $\tau$: And after sometime $t$, I introduced a constant magnetic field(let's imagine it spawned suddenly and ignored the change in flux from $t_o$ $\rightarrow$ ...
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Effects generated from a supercapacitor placed in a time varying external magnetic field?

The diagram above, showcases the simple outlook of a supercapacitor's interior and combining it with a full circuit loop. If an exterior magnetic field is introduced in all the operating states of a ...
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Is the relative number of electric field lines between two charges proportional to the difference between those two charges?

Let us consider a system of two unlike charges and suppose that the magnitude of the positive charge is greater that of the negative charge and call them a and b respectively. If that(asked in the ...
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The Electromagetic Tensor and Minkowski Metric Sign Convention

I am trying to figure out how to switch between Minkowski metric tensor sign conventions of (+, -, -, -) to (-, +, +, +) for the electromagnetic tensor $F^{\alpha \beta}$. For the convention of (+, -,...
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Difference in the direction of propagation of em wave [duplicate]

How are kx-wt and kx+wt in terms of the direction of the wave. I have been stuck at this or an hour, still can not find a definitive answer.
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Deriving current density from charge density

Sorry for the naive question, but in Jackson's book in Electrodynamics, exercise 9.10, they give the charge density for the transition of hydrogen from 2p to 1s, $$\rho=\frac{2e}{\sqrt{6}a_0^4}re^{-...
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Dipole Inside Cavity of A Spherical Conductor

Consider the following case: There is a short electric dipole placed arbitrarily inside a spherical cavity inside a solid,uncharged conducting sphere We need to find electric field at a point ...
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124 views

How can direction of electric field due to a moving charge be from the present position of charge?

According to Maxwell's Equations, the electromagnetic waves in vacuum travel at the speed of light $c$. While solving Maxwell's equations using Lorenz gauge conditions (or basically evaluating scalar ...
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The Meaning of Electromagnetic 'News' in Griffiths Book

In the Introduction to Electrodynamics book, by David J. Griffiths, 4th edition, page 60, the author makes the following statement: "it is not the position, velocity, and acceleration of Q right now ...
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Electric field of a line of Charge on it axis using electric potential

We have a line of charge with length $L$ and charge density $\lambda$ and we want to find its Electric field on a point $p$ with distance $d$ from one end of it using potential. I drew a picture like ...
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Energy momentum tensor of EM field written in symmetric form

I'm reading A. Zee's book, Einstein Gravity in a Nutshell. In problem 7 of chapter IV.2, it is said that the energy momentum tensor of the electromagnetic field \begin{align} T^{\mu\nu}=\eta_{\lambda\...
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How to calculate Average Electric Field for a microscopic filed in dielectric?

In Griffith's book in The chapter of Electric Fields in Matter (The field inside dielectric) , He has considered the Sphere of Radius R and for the inner dielectric element He used the field as $$\...
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Constants of motion of an electron in a harmonic electromagnetic field in free space

I have encountered a question in Classical Electrodynamics, as below: In free space, an electron, initially at rest at $z=0$, is subjected to an intense laser field $\vec E=\hat x A \cos(\omega t-...
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Why can infinite planes be approximated as Gaussian surfaces?

A little background: I'm an undergraduate studying Electrodynamics, currently in Chapter 8 of Griffiths. A question I came across (8.4 part a for those curious) asks for a calculation of the force ...
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Coulomb forces in String Theory

In QED electrostatic forces are mediated by field theoretic effects known as virtual "particles" if I am not mistaken, but I don't know how string theory explains electrostatic interactions between ...
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A changing magnetic field passes through a wire loop but the loop itself is not in the field. Is an EMF induced in the loop? [duplicate]

$$\nabla \times \vec{E} =-\frac{\partial{\vec{B}}}{\partial{t}}$$ Applying Stokes' theorem: $$\oint_{loop} \vec{E} \cdot d\vec{l}=\int_S -\frac{\partial{\vec{B}}}{\partial{t}} \cdot d\vec{S}$$ ...
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Does this example contradict Earnshaw's theorem in one dimension?

This is basically a continuation of the post here. Consider electrostatics in $1$-dimension (say, the $x$-axis). Now consider a positive charge $+q$ located at $x=0$, and two equal negative charges $...
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Facing a paradox: Earnshaw's theorem in one dimension

Consider a one-dimensional situation on a straight line (say, $x$-axis). Let a charge of magnitude $q$ be located at $x=x_0$, the potential satisfies the Poisson's equation $$\frac{d^2V}{dx^2}=-\frac{\...
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Are the microwaves in an ECRIS plane polarized?

Or randomly polarized? Are the photons in phase, like in a laser or maser? What is the theory behind how an electron in an ECRIS responds to a microwave photon?
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Space translation of coordinates, classical field theory

Consider the Lagrangian density $L = -\frac{1}{4}F_{\mu\nu}F^{\mu \nu}$ with $F_{\mu \nu} = \partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu} $. After deriving the Euler-Lagrange equations for this ...
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Divergence of current density and electric field within a wire

In the following exercise: I concern myself with the validity of my interpretations of (b). Here I am more confident slightly. The divergence of the current density is merely $- d \rho / dt$, so as ...
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Deriving magnitudes for $\mathbf J$ and $\mathbf E$ from the shape of a conductor

In the following exercise: I have no idea how to infer the magnitude of $\mathbf J$ nor $\mathbf E$ given the shape of the wire. The only clear thing to me here is that A, B and C all have different ...
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Destructive interference in vacuum (energy conservation) [duplicate]

The following question was proposed by a student durante a lecture for a grad course in EM. What happens to the energy of an EM wave during destructive interference in vacuum, in regards to the ...
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Formula for all the Lorentz boosts that result in $E$ parallel to $B$?

This is a follow-up question to a previous question regarding a minimum-energy invariant of the electromagnetic field. @ChiralAnomaly showed that there is indeed an invariant minimum energy density ...
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About density charged in the Liénard - Wiechert Potential to Point Charge?

I'm reading Griffiths Ch. 10. In the 10.3.1 section, there's a proof of this integral $$ \int \rho(r^\prime, t_r) \mathrm{d} \tau^\prime $$ which is not equal to the charge of the particle, but ...
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Relation between potential and charge of a group of conductors

studying electrodynamics I encountered a few weeks ago this statement regarding a set of conductors in space with no free charges: I could not find an explicit proof of this in any book and I did not ...
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Does the magnetic field move with the current element that induced it?

Initially, a point($P$) is defined in space, with a magnetic field($-B\hat{k}$) produced by a current element ($Idl$). If the wire begins to move in the $-v\hat{i}$ direction, would that produce an ...
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Is this a correct argument why $c$ is the cosmic speed limit, and what does it mean for the speed of massless particles? [closed]

I am now in my second bachelor, taking both an electrodynamics and a quantum mechanics course. This made me think of an argument to explain why particles cannot exceed the speed of light. So far I ...
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Different between spatial change in magnetic field & motional emf?

For the case of a stationary loop, and a changing magnetic field producing a non-conservative electric field $E_{nc}$: If the induced emf (${\Large{\varepsilon}}$) is due to both the change in ...
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Pressure radiation using Lorentz force

We know from theory and experiment that an electromagnetic wave that incides on a surface will generate a radiation pressure normal to that surface as a result of the change in momentum of the wave ...
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How to correctly differentiate the Lienard-Wiechert four-vector potential to get the EM tensor?

The retarded 4-vector potential for a moving charge is given by $$ A^\alpha = \left. \frac {eV^\alpha(\tau)}{V\cdot[x-r(\tau)]} \right|_{\tau = \tau_0} $$ where $e$ is the charge, $V$ the four-...
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How do we find the surface charge density of a charged conductor?

It is mentioned in Feynman volume 2 that it is quite algorithmic , where the surface charge density is first guessed then check whether it is equipotential at the metal surface.. My question is for a ...
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Conservation of magnetic charge

It is well known that the electric charge of a system can be thought of as the Noether charge associated with isotropic large gauge transformations. That is, given Einstein-Maxwell theory $$S=\frac{1}...