All Questions
Tagged with electromagnetism homework-and-exercises
1,552
questions
29
votes
6
answers
9k
views
Can a gym be built to supply electricity to homes? [closed]
A moving magnet induces a current in a conductor, then shouldn't we be able to generate electricity through manual labour?
I was thinking about building a gym that used magnets as weights. People ...
- 1,323
26
votes
3
answers
9k
views
Deriving the speed of the propagation of a change in the Electromagnetic Field from Maxwell's Equations
I've been told that, from Maxwell's equations, one can find that the propagation of change in the Electromagnetic Field travels at a speed $\frac{1}{\sqrt{\mu_0 \epsilon_0}}$ (the values of which can ...
- 6,000
21
votes
4
answers
41k
views
Derivation of self-inductance of a long wire
Currently I am stuck, trying to derive the self-inductance of a long wire. According to literature it should be
$$L=\frac{\mu_r\mu_0l}{8\pi}$$
and in literature its derived by looking at the energy ...
- 1,573
20
votes
3
answers
2k
views
Electromagnetism problem: where does the magnetic field come from?
Consider the following problem:
Consider a plane with uniform charge density $\sigma$. Above the said plane, there is a system of conducting wires made up of an U-shaped circuit on which a linear ...
- 571
18
votes
2
answers
22k
views
Is magnetic force non-conservative? [duplicate]
If magnetic field is conservative, then why not the magnetic force?
My professor thinks it is non conservative but he couldn't explain to me why?
- 181
15
votes
4
answers
57k
views
Transverse Magnetic (TM) and Transverse Electric (TE) modes
I'm reading and working my way through "Plasmonics Fundamentals" by Stefan Maier and I've come across a step in the workings that I'm struggling to understand when working out the electromagnetic ...
- 962
14
votes
4
answers
5k
views
Why are EM plane waves transverse?
I was reading Griffiths' Introduction to Electrodynamics, specifically Section 9.2.2 on plane waves. I can see that if we want a transverse wave traveling in the $z$ direction that we are only going ...
- 561
13
votes
9
answers
57k
views
What's the core difference between the electric and magnetic forces?
I require only a simple answer. One sentence is enough... (It's for high school physics)
- 245
13
votes
2
answers
5k
views
Deriving Biot-Savart Law from Maxwell's Equations
As an exercise, I've been trying to derive the Biot-Savart law from the second set of Maxwell's equations for steady-state current
$$\begin{align}&\nabla\cdot\mathbf{B}=0&&\nabla\times\...
- 838
13
votes
1
answer
560
views
How can I find the position of an image charge when the boundary is parabolic or hyperbolic?
If the position of some charge $Q$ is known, the boundary condition is $u=0$ on some parabolic surface, and we know the image charge has its electric volume of $Q'$, then how can I determine the ...
- 147
12
votes
2
answers
7k
views
Proving Gauge invariance of Schrodinger Equation
I am trying to proof explicitly that Schrodinger equation:
$$ i\hbar \partial_t \psi = \left[ -\frac{1}{2m}\left(\frac{\hbar}{i}\nabla-q\vec{A}\right)^2+qV \right]\psi$$
remains the same under the ...
- 980
12
votes
1
answer
3k
views
Lorentz force derivation in quantum mechanics [closed]
In Sakurai and Napolitano, chapter 2, there's a derivation of the QM Lorentz force.
Given $$H=\frac{1}{2m}\left(\mathbf{p}-\frac{e\mathbf{A}}{c}\right)^2+e\phi = \frac{\mathbf{\Pi}^2}{2m}+e\phi$$
...
- 877
12
votes
1
answer
453
views
Is the uniqueness theorem correct in superconductivity?
There is an uniqueness theorem in electromagnetism. It says that the solution of Maxwell's Equations is determined uniquely by boundary conditions.
We can treat superconductivity as a completely ...
- 1,191
11
votes
3
answers
2k
views
Propagator of Maxwell-Chern-Simons theory
I need to compute the "topologically massive photon" propagator.
I've started with:
$$
\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \frac{\mu}{4}\epsilon^{\mu\nu\lambda}A_\mu\partial_\nu ...
- 929
11
votes
1
answer
2k
views
Chern-Simons Energy-Momentum Tensor
I'm assuming the following statement is true. I'm not finding any reference which shows that explicitly.
Statement: Chern-Simons term is a topological one and does not contribute to the Energy-...
- 944
11
votes
1
answer
1k
views
Question about superconductivity
A long cylinder of radius $R$ is made from two different material. Its radius $r<r_0$
$(r_0<R)$ part is a material with superconducting transition temperature $T_1$, and its $r_0<r<R$ ...
- 1,191
10
votes
5
answers
6k
views
Why does a ring falling through a magnetic field experience an upward force?
The Problem states:
A metallic ring of Mass $M$ and radius $r$ falls freely under the influence of gravity in the direction along the negative Z-axis. A magnetic field $B_z = B_0(1-z\lambda)$ where ...
- 127
9
votes
5
answers
5k
views
Is gravity non-negligible compared to the electromagnetic force?
Consider two electrons approaching each other at rather fast speeds, maybe even coming close to colliding. Does gravity play any role in this event? If so, how much influence does it have? Do we need ...
9
votes
4
answers
668
views
Distribution of point charges on a line of finite length
How will $N$ freely moving charges confined to a line with length $L$ be distributed? What are their equilibrium positions?
- 4,194
9
votes
1
answer
860
views
Electron in the proximity of a magnetic monopole
I am puzzling about an exercise in the book "Electromagnetic Theory" by Ferraro (p.543).
An electron (mass $m$, charge $-e$) in a monopole magnetic field $\vec{B}\left(\vec{r}\right)=g\frac{\vec{r}}{...
- 393
9
votes
2
answers
2k
views
Why does the dimension of the electric charge depend on the number of spacetime dimensions?
We can find via dimensional analysis that the dimension of the electric charge varies with the dimension of space-time $(D+1)$:
$$[\text{charge}] = (\text{eV})^{(3-D)/2}.$$
It is dimensionless if ...
- 944
8
votes
3
answers
5k
views
Derivation of the speed of light using the integral forms of Maxwell's Equations
Having just finished physics 2, I've been (slightly) exposed to showing that light is a wave with speed $1/\sqrt{\mu _0 \epsilon _0 }$ using the differential forms of Maxwell's equations, though this ...
- 905
8
votes
1
answer
5k
views
The gauge-invariance of the probability current
It is simple to show that under the gauge transformation $$\begin{cases}\vec A\to\vec A+\nabla\chi\\
\phi\to\phi-\frac{\partial \chi}{\partial t}\\
\psi\to \psi \exp\left(\frac{iq\chi}{\hbar}\right)\...
- 81
8
votes
1
answer
406
views
Quantum Cyclotron Frequency - Why is it off by a factor of 2?
Say you have a magnetic field $\vec{B}=(0,0,B_0)$. Then the Schrodinger Equation Hamiltonian for a spin-2 particle of charge $e$ moving in this field is:
$$H = \frac{1}{2m}[\vec{p}-e\vec{A}]^2-\vec{\...
- 1,212
7
votes
2
answers
784
views
Approximating an expression for a potential
In a problem which I was doing, I came across an expression for the potential $V$ of a system as follows $$V = k\left(\frac{1}{l - x} + \frac{1}{l + x}\right)\tag{1}\label{1}$$ where $k$ is a constant,...
- 1,324
7
votes
1
answer
13k
views
How much power would it take to stop a bullet with a magnet?
If a 7.5 gram copper-jacketed lead bullet (say, a 9x19mm Parabellum) was travelling at 360 m/s, how much power would it take to diamagnetically stop it in the space of one meter?
This question comes ...
- 181
7
votes
2
answers
2k
views
Derivation of the quadratic form of the Dirac equation
I am asked to derive the quadratic form of the Dirac equation in an electromagnetic field,
$\left[\left(i\hbar \partial - \frac{e}{c}A\right)^2 - \frac{\hbar e}{2c} \sigma^{\mu\nu} F_{\mu\nu} - m^2c^...
- 475
7
votes
5
answers
1k
views
Hollow conductor containing charge: why is internal field cancelled outside and why are the field oustide the cavity zero inside the cavity?
I've a doubt on the following situation. Consider a hollow conductor $A$ (of arbitrary shape) containing another conductor $B$ (again of arbitrary shape), with a positive charge $+q$.
By the ...
- 2,617
7
votes
1
answer
1k
views
Homopolar motor and Lorentz force
My second grader thought making a homopolar motor for her science experiment would be fun. And, it was. Now I am trying to explain how it works and the Lorentz force. Please help me by giving me a ...
- 71
7
votes
1
answer
2k
views
Magnetic field from a half-cylinder [closed]
I am preparing for an exam, on this problem I had the opposite direction of the magnetic field.
A conductor-cylinder with radius R has been cut in half ($\phi \in [0,\pi]$)
A DC current $I$ runs ...
- 367