0
votes
1answer
36 views

Essay topic in classical electrodynamics [closed]

I am currently in a course of classical electrodynamics, and we have discussed Lorentz transformations and such. We need to write an essay on a free to choose topic, but I have no idea what an ...
1
vote
1answer
75 views

Step in a proof that $\textrm{div} \ \mathbf{B} = 0$ from Biot-Savart's law

Notation: The magnetic field $\mathbf{B}$ generated by a point charge $e$ moving with velocity $\mathbf{v}$ is given by Biot-Savart's law $$\mathbf{B} = \frac{\mu_0 e\ \mathbf{v} \wedge ...
1
vote
2answers
120 views

Integration constants in Maxwell's equations (ambiguousness?)

In classical electrodynamics, if the electric field (or magnetic field, either of the two) is fully known (for simplicity: in a vacuum with $\rho = 0, \vec{j} = 0$), is it possible to unambiguously ...
2
votes
7answers
483 views

Metallic and glass sphere of same size released at a height

This question was in my exam today : A metallic and glass sphere of same size were dropped at same height. Which sphere would hit the ground first and why? I have thought about several things and ...
0
votes
0answers
22 views

How does displacement current come about? [duplicate]

I know that displacement current is due to time-varying electric field and its not an electric current. But then, is it charge that is actually being displaced?
1
vote
1answer
24 views

Far Field Diffraction of EM waves: what does the zero frequency signify?

If you have a system of independently radiating electrons/point-charges, the far field distribution of the EM waves can be approximated by the fraunhoffer diffraction integral, or simply by the ...
1
vote
1answer
65 views

Does the 1-D poisson's equation have monotonic potentials if $\rho=\rho(\phi(z))$?

I am solving the 1-D poisson equation: $$\frac{d^2 \phi}{dz^2}=-4\pi\rho(\phi)$$ with the additional requirement that $\rho(\phi(z=0))=0$. If I start by multiplying each side by $\frac{d\phi}{d z}$ ...
3
votes
2answers
95 views

Can the $\vec H$-field have non-zero divergence? Does an $\vec H$-field monopole exist?

We know that, $\vec \nabla \cdot \vec B=0$ but $\vec \nabla \cdot \vec H\neq 0$, if $\vec \nabla \cdot \vec M \neq 0$. Does it mean that, in those cases $\vec H$-field has poles although $\vec ...
1
vote
1answer
50 views

electromagnetic induction. Does charge matter?

Just wondering. I know a negative electric charge moving though a coil will induce a voltage in the coil. My question is, would a positive charge, say an ion beam, moving though a coil also induce a ...
10
votes
2answers
264 views

The problem of self-force on point charges

Allow me to preface this by stating that I am a high school student interested in physics and self-studying using a variety of resources, both on- and off-line, primarily GSU's HyperPhysics website, ...
1
vote
1answer
72 views

The workings of the Hall effect?

I want to ask about the workings of the Hall effect. Why do the electrons come to rest on the edge of the wire? The magnetic field pushes them up, and the electric field pushes them forward. Shouldn't ...
2
votes
4answers
149 views

Is the canonical momentum conserved when a particle moves in magnetic field?

Here is a question about the canonical momentum that I had asked some days ago, but I still have one point that I am not understand. Considering a particle moves in a magnetic field with charge $q$ ...
1
vote
1answer
116 views

Frequency of rotating coil

Given a coil initially in the x-y plane, rotating at angular frequency $ \omega $ about the x-axis in a magnetic field in the z-direction. This uniform time varying magnetic field is given by $B_z ...
1
vote
2answers
103 views

A question about canonical momentum and arbitrariness for potential in magnetism

The following question confuses me: There exists magnetic field $B_z =- \beta x$ where $x > 0$, and a particle is incident from origin point $(0,0)$ with pisitive charge $q$, mass $m$, and ...
2
votes
3answers
120 views

Why do surfaces act like barriers for electrons?

Say you have a conductor, filled with free electrons. The nuclei have a weak pull on the valence electrons so they are moving around in the conductor. But the electrons don't leave the solid. If you ...
0
votes
0answers
114 views

Field inside a conductor?

If the above image is a cross section of a conductor, the field at the point shown is not zero. So the field inside a conductor is not zero at all points. You could argue that the electrons would ...
3
votes
1answer
97 views

Is Newton's third compatible with retarded Lorentz force?

In Griffiths Introduction to electrodynamics it is said that Newton's third law is not valid in electrodynamics, but, in the example given, the it does not consider the retarded values for the fields ...
1
vote
0answers
77 views

Complex polarizability of a dielectric sphere in a homohenious electric field

It is well known that complex polarizability of uniform dielectric sphere with radius $r$ and complex permittivity $\hat\epsilon_{in}(\omega)$ placed in a medium with complex permittivity ...
0
votes
1answer
51 views

Objects made up of electrons?

Say you have a neutral rod, and you bring a positively charged rod beside it (call the side the charged rod is brought near side A and the other side side B). The electrons from the side B will start ...
2
votes
1answer
43 views

Is charge 'localization' implicit in the idea of current?

If it was possible for charge to assume arbitrary densities, like we often see electrostatic exercises, and one could spread charge density uniformly over a ring, then how one would, theoretically, ...
3
votes
1answer
128 views

Missing terms in Hamiltonian after Legendre transformation of Lagrangian

Short question Given any Lagrangian density of fields one could possibly conceive, is it the case that after one has performed a Legendre transformation, if the Hamiltonian is then expressed in terms ...
0
votes
0answers
32 views

Is it physically realistic to have an electric field and polarisation density but no displacement field?

Given a Lagrangian density that describes a classical dielectric in interaction with the EM field, I found the Euler-Lagrange equations, and in the case of the electric field, worked through to find ...
4
votes
2answers
115 views

In Jackson's expression for the electrostatic Green function, why is the Laplacian taken with respect to the primed coordinates?

Jackson writes, The function $1/|\mathbf{x} - \mathbf{x}'|$ is only one of a class of functions depending on the variables $\mathbf{x}$ and $\mathbf{x}'$, and called Green functions, which satisfy ...
3
votes
1answer
79 views

Motion in a Paul trap: $2n$th harmonic with larger amplitude than $n$th harmonic

Using a Paul trap, we captured the motion of a light charged particle (based on a rotating potential applied by AC current). Our rotational frequency was 50 Hz, and so when used FFT on the data, we ...
1
vote
1answer
106 views

Traditional Kirchoff voltage law in AC circuit?

The traditional (not taking into account phasor addition or complex addition) application of Kirchoff Voltage law, i.e. $\Sigma\Delta V=0$ along a loop, does not work for AC circuits. We can sum the ...
3
votes
1answer
169 views

Is there a Hamiltonian for the (classical) electromagnetic field? If so, how can it be derived from the Lagrangian?

The classical Lagrangian for the electromagnetic field is $$\mathcal{L} = -\frac{1}{4\mu_0} F^{\mu \nu} F_{\mu \nu} + J^\mu A_\mu.$$ Is there also a Hamiltonian? If so, how to derive it? I know how ...
8
votes
2answers
179 views

What is the mechanism by which magnetic fields do work?

I've seen some conflicted answers to this question in texts and on the web, in the case of a dipole, for example. Do magnetic fields do work directly, or is it their induced electric fields that do ...
0
votes
1answer
98 views

How is bound charge and free charge possible?

I am studying Introduction to electrodynamics by Griffiths and I came along a concept I cannot seem to understand properly. The concept of free charge AND bound charge. I do not understand how we can ...
2
votes
2answers
64 views

What is the area in Faraday's law if we have only a piece of metal moving in a magnetic field?

If a piece of metal of length $l$ is moving with a speed $v$ in a region where there is a uniform magnetic field $B$ perpendicular to it, there will be a potential difference across its terminals ...
-1
votes
1answer
38 views

Scalar Field of a long thin wire

Given the situation that $B=-\nabla A$ where B is magnetic field and A is some Scalar Field. How can I calculate the scalar field, A. We are dealing with current free region, here. I know we can ...
3
votes
1answer
126 views

Orthogonality between $\vec{E}$ and $\vec{H}$ waves with space-dependent amplitudes

I am able to prove in a few lines that the electrodynamic field vectors $\vec{E}$, $\vec{H}$ and $\vec{S}$ are all orthogonal to each other considering that $\vec{E}$ and $\vec{H}$ are coherent plane ...
4
votes
2answers
325 views

Electrostatics/ magnetostatics: why is $\int_{all space} d\vec r \; \nabla \cdot(\vec A \times \vec B)$ equal to 0?

I'm reading electrodynamics notes and come across that: $$\int_{all space} d\vec r \; \nabla \cdot(\vec A \times \vec B)=0$$ in case of magnetostatics and : $$\int_{all space} d\vec r \; \nabla ...
4
votes
1answer
241 views

What is the magnitude of the force on a charged particle due to electromagnetic radiation?

Suppose there is an electromagnetic wave moving forward in the $\mathbf{\hat{k}}$ direction. Its electric/magnetic field components are given by: $$\mathbf{E} = E_0 \sin(kz - \omega t) ...
0
votes
2answers
83 views

Drift Speed and Current in Two Different Inertial Frames

We have a long, cylindrical wire carrying a constant current I in an inertial frame. At a distance of R from the center of the wire, the magnitude of magnetic field is $μI/2πR$. What is the magnitude ...
1
vote
1answer
82 views

Accelerated charge inside sphere (again!)

Sorry to go on about this scenario again but I think something is going on here. Imagine a stationary charge $q$, with mass $m$, at the center of a stationary hollow spherical dielectric shell with ...
1
vote
1answer
45 views

Is there a heuristic argument for the expression $ \textbf{g} = \frac {\mathbf{S}}{c^2}$?

Electromagnetic momentum density and the Poynting vector are related by the simple expression: $$ \textbf{g} = \frac {\mathbf{S}}{c^2}$$ It can be rigorously derived from Maxwell's equations, but is ...
3
votes
0answers
81 views

Accelerated electromagnetic system leads to divergent calculation?

Consider the above system comprising a pair of oppositely charged parallel plates, connected by a rigid rod of length $r$, constrained to move in the x-direction. The forces on the plates from the ...
3
votes
2answers
243 views

When studying electrodynamics do we assume Maxwell's Equations or derive them?

This question is because something made me confused. I always thought that the idea behind electrodynamics was to postulate some things, like Coulomb's law in electrostatics and so on, and then ...
2
votes
1answer
157 views

Why is there no (time derivative of charge density) in the $B$ field in Jefimenko's equations?

I was going through Griffiths chapter on potentials and fields just to brush up on a few old things. He gets to Jefimenko's equations by this general path: Maxwell's equations Introduce scalar and ...
7
votes
4answers
326 views

Why does electric field intensity $E$ can be uniquely determined by its divergence and curl? [duplicate]

My question is, the number of following equations $$\nabla\cdot E=\frac{\rho}{\varepsilon}$$ $$\nabla\times E=-\frac{\partial B}{\partial t}$$ is 4 while the number of unknown variables ...
-3
votes
1answer
2k views

What causes electron to orbit the nucleus in an atom? [closed]

What causes the electron to orbit the nucleus? Which is the force that causes it to do so? Is it related to the Electro - Magnetic force? .
2
votes
1answer
66 views

What is the intensity of this light?

I am struggling with a derivation that calculates the cross sections for Mie scattering and since the incident light is considered to be a x-polarized plane wave I thought that we would have $$I_i = ...
6
votes
3answers
548 views

How do I calculate electric fields due to currents of magnetic dipoles?

Short version of my question: Do dipole currents cause fields? I think currents of aligned magnetic dipoles cause an electric field, but I don't know how to calculate this field except in the ...
4
votes
2answers
97 views

Applicability of the concept of voltage in electrodynamic circuits

In electrostatics, we have $$\nabla \times \vec{E} = 0$$. Hence, we can define a scalar potential $V$, where $$\vec{E} = -\nabla V$$. We know from Faraday's law that $$\nabla \times \vec{E} = ...
2
votes
0answers
62 views

Mie Scattering for spheres with constant dipole moment

I was wondering whether there exists a theory that describes Mie Scattering for spheres that have a constant dipole moment. Since there are theories that describe Mie scattering in the case of a ...
1
vote
1answer
314 views

General solution to the Helmholtz wave equation with complex-valued frequency in cylinderical coordinates

The Helmholtz equation is expressed as $$\nabla^2 \psi + \lambda \psi = 0$$. This equation occurs, for eg., after taking the Fourier transform (with respect to the time coordinate) of the wave ...
1
vote
1answer
212 views

Understand equations of a conducting sphere

Can somebody explain to me, when the following two equations (equations 2.48 and 2.50 in this document) are applicable and what $\Phi_s$ and $\Phi$ actually are? The thing is, I want to find general ...
0
votes
0answers
89 views

Potential energy: Electric field two spherical charges

I want to determine the potential energy of two equally charged spherical charges by using the equation: $V_{pot}= \int_V \frac{1}{2} \epsilon_0 E^2 dV$ and therefore I was wondering what I has to ...
0
votes
1answer
87 views

Electric dipole, error in calculation

Currently I am calculating the dipole moment of a metal sphere in a uniform electric field $E_0$ in z-direction. From here I know that the charge density look at page 15 is given by $ 3 \epsilon_0 ...
1
vote
0answers
63 views

Electric field screening for arbitrarily formed charge

if I have a not necessarily homogenous electric field of a charge distribution in an electrolyte and i want to find out what the electric field at some position in the electrolyte is. is there any ...