All Questions
Tagged with electromagnetism homework-and-exercises
1,550
questions
1
vote
2
answers
123
views
How to compute the resistance of a nonuniform cylinder with varying resistivity?
The generally quoted formula foe resistance is
\begin{equation}
R = \rho \ell/A
\end{equation}
some special cases are easy to solve. For example the case where the current flowing along the z-axis and ...
- 196
0
votes
0
answers
63
views
What does it mean by "physical field"?
I'm attempting a question about the Stern-Gerlach experiment where an electron is used with an assumed up-spin state in a non-uniform magnetic field. It asks us to talk about the dynamics of this ...
- 11
1
vote
0
answers
18
views
EMF generation by rotating rod without magnetic field [closed]
what is the EMF generated by a conducting rotating rod of mass $m$ and length $l$ in free space without magnetic field. the rod is roating with angular speed $w$? also find the current if the rod has ...
0
votes
1
answer
34
views
How to find the capacitance between two metal sheets [closed]
Let’s say I have two metal sheets in a 2D plane. The first one has area A, the second one is infinitely long, and they are separated from each other by a distance d. How can I find the capacitance ...
0
votes
2
answers
129
views
Electromagnetism [closed]
A positively charged particle travels horizontally northward and enters a region where a field may exist. This region may contain only a magnetic field, only an electric field, or both a magnetic ...
2
votes
2
answers
151
views
Derivation of propagator for Proca action in QFT book by A.Zee
Without considering gauge invariance, A.Zee derives Green function of electromagnetic field in his famous book, Quantum Field Theory in Nutshell. In chapter I.5, the Proca action would be,
$$S(A) = \...
- 629
0
votes
0
answers
54
views
Where does the $\eta^{\mu\nu}$ come from? (Maxwell Lagrangian, QFT) [duplicate]
From the Lagrangian in Maxwell theory
$$L = -\frac{1}{2}(\partial_{\mu} A_{\nu})(\partial^{\mu} A^{\nu}) + \frac{1}{2}(\partial_{\mu}A^{\mu})^2 - A_{\mu}J^{\mu}$$
I have to calculate $\frac{\partial L}...
- 361
2
votes
3
answers
206
views
Deriving continuity equation from 4-current of a charged particle
how can i check that following 4-current for a single charged particle
$$j^{\mu}(x)=qc\int d\tau u^{\mu}(\tau)\delta^{4}(x-r(\tau))$$
satisfies continuity equation $$\partial_\mu j^\mu = 0.$$
user391340
0
votes
1
answer
140
views
Dummy index question
The Maxwell's Lagrangian density is given by the equation, $$\mathcal L = -\frac{1}{4} \space F_{\mu\nu} \space F^{\mu\nu},$$ where $F^{\mu\nu} = \partial^\mu A^\nu - \partial^\nu A^\mu$.
Hence, one ...
- 171
2
votes
1
answer
65
views
Canonical electromagnetic stress-energy-momentum tensor
I have canonical electromagnetic stress-energy-momentum tensor defined as:
$T_{\mu\nu}=\frac{1}{4}\eta^{\mu\nu}F_{\alpha\beta}F^{\alpha\beta}-F^{\mu\lambda}F^{\nu}_{\,\,\lambda}-F^{\mu\lambda}\...
- 23
1
vote
0
answers
92
views
Relativistic equations of motion in uniform electric field through matrix exponentiation
For my undergraduate studies, I was faced with the problem of finding the equations of motion for a particle subject to a uniform electric field, in the relativistic case. I would like to follow the ...
- 25
-2
votes
1
answer
76
views
Where is this circular loop attracted? [closed]
A circular loop carrying current "I" in anti-clockwise direction is placed between two straight and parallel wires each carrying current I. Ignoring the force of the straight wires on each ...
- 119
1
vote
1
answer
62
views
'Thin' conducting plate ambiguity
The situation at hand:
We have an infinite, thin conducting, grounded ($V=0$) plate at $z=0$.
Point charge (with charge +$Q$), at $z = a$.
How exactly are the charges distributed? I used the method ...
2
votes
1
answer
192
views
Dot product of the electric and magnetic field as the contraction of the electromagnetic tensor and its dual
I've see in some examples, e.g. here, that $$-4i\vec{E}\cdot \vec{B}=\tilde{F}_{\mu\nu}F^{\mu\nu}$$
How would you show such a relation? By inserting terms by terms inside this equation I've seen it is ...
- 941
6
votes
3
answers
2k
views
What property of light allows it to propagate in space? [closed]
I got this question in a university entrance exam; I'm not sure what could've been the answer. I've scoured the web and could hardly find a decent answer. The question and choices were:
What property ...
0
votes
1
answer
36
views
Potential of an alternating electric field in a capacitor
My question comes from a problem of electrodynamics where there's a relativistic particle with a given 4-momentum ($p^\mu=(\varepsilon,\vec{p})$) which enters a capacitor with an alternating electric ...
0
votes
1
answer
86
views
What would be the Joule requirement to a railgun launch a conventional bullet at mach 7?
The railgun project from the US Naval Surface Warfare Center Dahlgren Division shoots a projectile of 3.2kg at a speed of mach 7 with 18.4 megajoules of energy.
How many joules would a railgun need to ...
- 277
2
votes
1
answer
101
views
Primary constraint of electrodynamics
I have some problems understanding the transition from the Lagrangian to Hamiltonian formalism of electrodynamics. I will use the metric $(-+++)$.
I want to start from the Lagrangian which is ...
1
vote
1
answer
97
views
Magnetic Scalar Potential of Infinite Wire
While working on a question about magnetic scalar potential, I encountered a challenge. The question posits that the magnetic scalar potential, denoted as $\phi$, takes the form $\phi = -\frac{I}{2\pi}...
0
votes
2
answers
247
views
The origin of energy density formulas in Maxwell's electromagnetism
I am looking at the derivation of Poynting theory in Electrical Engineering texts and they usually start by the two statement:
$$W_e = \int_V\frac{1}{2}(\vec{E}.\vec{D})\,\,dv$$
$$W_m = \int_V\frac{1}{...
- 126
1
vote
0
answers
40
views
Detailed derivation of the energy-momentum tensor from the Maxwell Lagrangian [duplicate]
I have started studying QFT, and I am currently reviewing briefly on the classical field theory. I have come across the Maxwell Lagrangian given by
$$
\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}.
$$
...
- 35
0
votes
0
answers
29
views
Non-standard circuit
I partially solved this problem.
Problem: A charged sphere of radius $a$ is connected through a resistance $R$ to the earth. An electronic flow breaks out towards the sphere of infinity at speed $v$ ...
0
votes
1
answer
93
views
Momentum conservation in charged particles scattering
I'm studying a problem involving the scattering of two charged particles, A and B, with a mass ratio of 1:4 and identical charges. The particles move towards each other with equal and opposite ...
- 864
3
votes
3
answers
113
views
Finding the vector potential
$$\nabla\times\mathbf{B}=\nabla\times\left(\nabla\times\mathbf{A}\right)=\nabla\left(\nabla\cdot\mathbf{A}\right)-\nabla^2\mathbf{A}=\mu_0\mathbf{J}\tag{5.62}$$
Whenever I try to work this out and ...
- 220
0
votes
1
answer
49
views
Why can the current in this region be represented as this formula?$I_{in}=I-I\frac{r^2-b^2}{c^2-b^2}$ [closed]
An air coaxial transmission line has a solid inner conductor of radius a and an outer conductor of inner radius b and outer radius c. Find $\vec B$ as a functions of radial distance r.
The region in $...
- 51
1
vote
1
answer
63
views
Derivation of the ring charge from a disk charge with a hole
I am doing a problem in which I am given a uniformly charged disk, charge density $\sigma$, with radius $b$ and a concentric hole of radius $a$ in the $xy$ plane. A part of the problem I would have to ...
- 11
5
votes
3
answers
595
views
Two balls are dropped from the same height. Ball A is metallic and B, made up of an insulating material. Which of them touches ground first? [closed]
General motion under gravity states that both of them reach the ground simultaneously. But here, ball B reaches first. I searched for the solution but couldn't find any. Does it have anything to do ...
- 61
0
votes
1
answer
234
views
How does the Lagrangian work with a magnetic field?
I was told the following Lagrangian is for a charged particle with spin moving in a constant magnetic field:
$$
L = \frac{\left ( \vec p \right ) ^2}{2m} + \vec \mu \cdot \vec B$$
Let's just say $B$ ...
- 59
0
votes
2
answers
499
views
Should a wire loop moving through a constant rectangular magnetic field directed perpendicular to it's motion have zero induced current in the middle?
Suppose we have a loop of copper wire moving perpendicularly through a constant finite rectangular magnetic field directed into the screen .
When the loop enters the field, the induced current would ...
- 1
1
vote
1
answer
250
views
Does an emf in an aeroplane's wings result in a current? [closed]
In part (b) of this question, they have stated that the current that flows through the aeroplane is 0.00 A. When you use the value for emf from part (a) and the resistance, you can calculate that I = ...
- 31