All Questions
Tagged with electromagnetism homework-and-exercises
258
questions with no upvoted or accepted answers
4
votes
0
answers
67
views
Purcell/Morin: Why is approximating the resistance of a tapered rod using disk slices in series not adequate when the taper occurs very quickly?
The following exposition and question are based on two problems from the book "Electricity and Magnetism" by Purcell and Morin (problems 4.32 and 4.6 from Chapter 4 called "Electric ...
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4
votes
0
answers
1k
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Landau quantization: degeneracy of first level
In some books the degeneracy of one Landau level in a two-dimensional gas of free electrons is calculated in the following way:
Note: The electron spin is not considered.
Number of states of a free ...
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4
votes
3
answers
351
views
Magnetostatics or dynamics?
A spherical conductor, carrying a total charge $Q$, spins uniformly and very rapidly about an axis coinciding with one of its diameters. In the diagrams given below, the equilibrium charge density on ...
- 1,389
3
votes
1
answer
155
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Non-linearities in Lagrangian of a scalar field coupled to point-like source
I have an exercise where I did not manage to understand the questions. Basically, I have this Lagrangian
\begin{equation}
\mathcal{L}=\frac{1}{2}(\partial \pi)^2-\frac{1}{\Lambda^3}(\partial \pi)^2\...
3
votes
0
answers
629
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Poynting theorem on an example?
I understand the basic statement of Poynting theorem of conservation of energy relative to electromagnetic field.
However, I fail to apply it to an example.
Consider this classical case:
...
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3
votes
0
answers
174
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Question about the fields in a solenoid
I am very familiar with using Ampere's Law to find the B field inside a solenoid ($\mu_0nI(t)$). Then I can use Faradays to find the E field inside ($\propto\dot I$).
I want to get this result ...
- 1,788
3
votes
0
answers
88
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Charge distribution and potential in a 1-dimensional quasistatic system
Suppose you have an 1-dimensional system with a charge distribution $\rho(x)$ (not given) moving with an speed $v(x)$ (not given), calculate the potential $\phi(x)$ and the charge distribution $\rho(...
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3
votes
0
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378
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Angular momentum of particle in dipole magnetic field
Basically I'm just trying to find the expression for the angular momentum of a particle of mass $m$ and charge $q$ in a dipole magnetic field. In cylindrical coordinates, $\vec{v}=v_{\rho}\hat{\rho}+...
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3
votes
0
answers
339
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Bandgap Spacing in Photonic Crystals
I am doing some self-study on photonics and have encountered the following question:
We know that amorphous electronic crystals such as amorphous silicon have a bandgap. Can amorphous photonic ...
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3
votes
1
answer
1k
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Distribution of current of a rotating cone
If I have a hollow cone (surface with no bottom cover ) as the one in the picture. The cone has surface charged density $\sigma$. It rotates around the symmetry axis with an angular velocity $\omega$. ...
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2
votes
0
answers
57
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Charged pendulum and a fixed point charge
!My set-up is the following: i have an iron bolt suspended on a string next to an electromagnet, of which I steadily increase the voltage and thereby the magnetic field. Supposing the force is linear ...
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2
votes
1
answer
101
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Primary constraint of electrodynamics
I have some problems understanding the transition from the Lagrangian to Hamiltonian formalism of electrodynamics. I will use the metric $(-+++)$.
I want to start from the Lagrangian which is ...
2
votes
1
answer
134
views
Charged particle in a purely radial magnetic field, is the canonical angular momentum conserved?
Let $ \vec{B} = k \dfrac{\vec{u_r}}{r^2}$ (assuming magnetic monopoles exist) and let $q$ be a charged particle. The associated hamiltonian is $H = \dfrac{(\vec{p} - q \vec{A})^2}{2m}$ and the ...
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2
votes
0
answers
111
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How do I calculate the functional derivative of the EM action on the curved spacetime with respect to the metric?
I am having trouble with computing the functional derivative with respect to the metric of the EM on a curved spacetime:
\begin{equation}
S:=\frac{1}{16\pi^2 G}\int R \sqrt{-g}\text{ }d^4x-\frac{1}{4}\...
- 1,669
2
votes
1
answer
131
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Fermion number non-conservation in parallel $E$ and $B$ fields
This is from Problem 19.1 in Peskin and Schroeder.
(a) Show that the Adler-Bell-Jackiw anomaly equation leads to the following law for global fermion number conservation: If $N_R$ and $N_L$ are, ...
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2
votes
1
answer
58
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Manipulation of the diffusive term in MHD induction equation
I am trying to solve the magnetohydrodynamic (MHD) equations with a spatially varying resistivity, $\eta$. To remove some of the numerical stiffness from my finite volume approach, I am trying to get ...
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2
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0
answers
154
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Debye length for a debye shield
I understand debye length and even the concept of debye shielding, but quantitatively I'm a little confused. If the debye shield has a potential of $$\Phi=\frac{q}{4\pi\epsilon_{0}r}\exp\left({\frac{-...
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2
votes
1
answer
51
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Questions on Forces involved in oscillating mass dipole
Say we have two balls of radius $R$ on both sides of a massless dielectric rod and it starts oscillating due to an external electric field. Other than the external field would there be an electric ...
2
votes
0
answers
118
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Magnetic field due to a double tape line
I have been asked to calculate the inductance of a double tape line :
Now we know that $$ N\phi = LI$$
So let's calculate the magnetic field by assuming an amperian loop like this:
$$\int B.dl = ...
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2
votes
0
answers
406
views
Derivation of Coulomb's law from classical field theory
In the section on Coulomb's law in QFT by Schwartz, he expands $-\frac{1}{4}F_{\mu\nu}^{2}$ to get $-\frac{1}{2}(\partial_{\mu}A_{\nu})^{2} + \frac{1}{2}(\partial_{\mu}A_{\mu})^{2}$, can someone ...
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2
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0
answers
132
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Input impedance of a line with complex load
I am currently studying electromagnetism mostly with the help of the book "Microwave Engineering" and when trying to solve problems which main goal is to compute the input impedance of a lossless ...
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2
votes
1
answer
69
views
Faraday Tensor quadruple product
I would like to compute the following:
$$F^{ab}F_{ac}F_{bd}F^{cd}$$
Is this equal to $4(E^2-B^2)^2?$
If so how can i quickly calculate it as such?
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2
votes
1
answer
145
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How to prove this matrix differential for Born-Infeld theory?
Consider the Born-Infeld Lagrangian, page 30 of Born-Infeld Action and Its
Applications by Cong Wang.
$L_{BI} = \sqrt{\det (1+ F)}$ where $F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$. I ...
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2
votes
3
answers
823
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Why does voltage cancel out if a circuit is going through a magnetic field?
The answer says that there is no current as there is no voltage, but why is there no voltage even though they cut field lines?
EDIT; I found the answers, but still not really understanding it
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2
votes
0
answers
102
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Possible Magnets
Okay so I was going through my book and found this interesting question --
Which of the following is possible?
$a)$ a magnet with no poles
$b)$ a magnet with two poles
$c)$ a temporary magnet ...
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2
votes
0
answers
154
views
One from Landau's Minimum (Macroscopic Electrodynamics)
A dielectric
sphere with the electric and magnetic susceptibilities ε1 and µ1 is rotating with
angular frequency ω in a constant electric field E~ in a medium, characterized
by the parameters ε2 and ...
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2
votes
0
answers
208
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Second-order correction in Quantum-Confined Stark effect
In the wikipedia article, there is a second-order correction in the Quantum-Confined Stark Effect. I could not understand how it was solved. I did not understand the meaning of 2(0) and 1(0) and how I ...
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2
votes
0
answers
492
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Motion of a charged particle in a "solid" charged sphere (accounting for radiation)
Consider a particle (point charge) with charge $q$ and mass $m$ that crosses into a uniformly charged sphere (with charge $Q$ and radius $R$). The trajectory of the particle is a diameter of the ...
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2
votes
0
answers
480
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Magnetic flux density a small distance off axis from a current loop
I'm currently studying physics at University and struggling with the problem mentioned, it's on a past paper I'm trying to do.
I have calculated the B field on axis as (sorry don't know how to format ...
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2
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0
answers
1k
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Hysteresis Curve and how to implement it using Preisach model or other models
As a homework I need to draw a hysteresis curve (preferably an interactive one) using Matlab or any other programming language. The problem is I have trouble finding a good algorithm to do so. I need ...
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2
votes
0
answers
885
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Finding the terminal velocity of a magnet dropped in a solenoid
We have to find proportionality of the terminal velocity with the factors of the system:
Plot: a small dipole(mass $m$) with dipole moment $\mu$ is dropped in a long solenoid (radius $r$, ...
- 2,479
2
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0
answers
886
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Solar wind and the Earth's magnetic field
I have again an old question from a comprehensive exam I took a couple of months ago. Lucky for me one could pick 5 out of 8 questions, because on some of the problems I didn't even know how to start. ...
- 14.9k
2
votes
0
answers
205
views
Wave propagation in anisotropic media
I'm given a wave propagation in an anisotropic medium with the following properties:
$\epsilon=\left[\begin{array}{ccc} \epsilon_{11} & 0 & 0 \\
\epsilon_{21} & \epsilon_{22} & \...
- 2,897
1
vote
0
answers
60
views
Vector potential of Weird loop
I have to calculate the vectorpotential of a current flowing through the loop at the origin:
where the current is given by $I(t)=kt$ for some $k>0$.
Given equations
$$\mathbf{A} = \frac{\mu_0}{4\...
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1
vote
1
answer
102
views
Perturbation of central field potential
i`d like to consider system with Coulomb potential: $U = -\frac{\alpha}{r}$ and constant magnetic field.It is easy to write Lagrangian function:
$$ L = \frac{m}{2}(\dot{\rho}^2 + \rho^2\dot{\phi}^2) + ...
1
vote
0
answers
132
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Coilgun projectile force calculation
Please excuse me if I am completely wrong because I am a 9th grader but I hopefully am able to explain briefly about my problem. I was trying to create a function to calculate the Force of an iron ...
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1
vote
1
answer
49
views
How can I estimate the force of an electromagnet?
I am doing an experiment on electromagnetism, basically I am just testing the pulling force of an electromagnet using a newton meter with a magnetic hook and seeing how the pulling force changes as i ...
- 11
1
vote
0
answers
92
views
Relativistic equations of motion in uniform electric field through matrix exponentiation
For my undergraduate studies, I was faced with the problem of finding the equations of motion for a particle subject to a uniform electric field, in the relativistic case. I would like to follow the ...
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1
vote
1
answer
97
views
Magnetic Scalar Potential of Infinite Wire
While working on a question about magnetic scalar potential, I encountered a challenge. The question posits that the magnetic scalar potential, denoted as $\phi$, takes the form $\phi = -\frac{I}{2\pi}...
1
vote
0
answers
55
views
Finding the equation of motion for vector potential $A_{\mu}$ in topologically massive electrodynamics
Essentially I want to vary the action
$$
S_M = \int d^3x \sqrt{-g} \left[- \frac{1}{4} F^{\mu \nu} F_{\mu \nu} - \frac{\alpha}{2} \epsilon^{\mu \nu \rho} A_\mu F_{\nu \rho} \right]
$$
with respect to $...
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1
vote
0
answers
74
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Confusion regarding magnetic length
Consider the geometric length of a magnet to be $L$ and magnetic length to be $L'$.
Some sources claim that $L'$ = $(0.84)L$.
One such claim can be found here:-
I cannot find any good reason to be ...
user355398
1
vote
0
answers
72
views
Electromagnetic waves in medium with strange polarization vector
I have an exercise in Electromagnetic waves, basically to find the refractive index of a wave in a medium with polarization $\mathbf{P}=\alpha \nabla \times \mathbf{E}$. I used the Maxwell equations ...
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1
vote
0
answers
63
views
Help with local gauge transformation
I have to prove that the following Lagrangian is invariant under local gauge transformation ($\psi\to e^{-i\lambda(x)}\psi$ and $A_\mu\to A_\mu+\partial_\mu\lambda(x)$, where $\lambda$ is real): $$\...
1
vote
1
answer
160
views
Showing that dirac delta point charge densities is covariant
Consider a point charge $Q$ with a trajectory of $\textbf{s}(t)$ in frame $O$. The densities are:
$$\rho(\textbf{x},t) = Q\delta^{(3)}(\textbf{x} - \textbf{s}(t))$$
$$\textbf{J}(\textbf{x},t) = Q\...
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1
vote
0
answers
261
views
Magnetic field due to circular surface current density
I am trying to find the magnetic field between two coaxial cylindrical shells of radius $a$ and $b$ respectively. They have a surface current density of $K = K_0cos(\theta)\hat{\theta}$ and $K=-K_0cos(...
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1
vote
0
answers
413
views
Capacitance of a thin conducting ring
I am following an exercise in which the capacitance of a thin ring is computed. The ring has radius $b$ and thickness $2a$ where $a<<b$.
In this exercise they compute the potential due to a ...
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1
vote
0
answers
44
views
When and how will charged oscillating pendulum in vacuum and Earth gravity stop?
Let's say there is a positively charged metallic sphere hanging on a thread in Earth's gravity and in vacuum. There is no electric field (except for the field from the sphere itself), no friction etc. ...
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1
vote
1
answer
147
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Is the closed contour integral of the Lorentz's Force equal to charge * EMF of the circuit?
I have a situation as pictured
That is, a rotating rectangular spire subject to an uniform magnetic field $\vec{B}$ (The rods to which it is attached and make the system spin is non-conductive, so it ...
1
vote
0
answers
51
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Equations of Motion for Hidden Photon
I was reading a paper called Parametrically enhanced hidden photon search by Peter Graham et al. In the paper, a Lagrangian that describes the theory of the hidden photon is
$$\mathcal{L}=-\frac{1}{4}(...
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