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 ...
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 ...
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 ...
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 ...
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?
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 ...
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 ...
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)
13
votes
2
answers
5k
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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
$$\begin{align}&\nabla\cdot\mathbf{B}=0&&\nabla\times\...
13
votes
1
answer
560
views
How can I find the position of an image charge when the boundary is parabolic or hyperbolic?
If the position of some charge $Q$ is known, the boundary condition is $u=0$ on some parabolic surface, and we know the image charge has its electric volume of $Q'$, then how can I determine the ...
12
votes
2
answers
7k
views
Proving Gauge invariance of Schrodinger Equation
I am trying to proof explicitly that Schrodinger equation:
$$ i\hbar \partial_t \psi = \left[ -\frac{1}{2m}\left(\frac{\hbar}{i}\nabla-q\vec{A}\right)^2+qV \right]\psi$$
remains the same under the ...
12
votes
1
answer
3k
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Lorentz force derivation in quantum mechanics [closed]
In Sakurai and Napolitano, chapter 2, there's a derivation of the QM Lorentz force.
Given $$H=\frac{1}{2m}\left(\mathbf{p}-\frac{e\mathbf{A}}{c}\right)^2+e\phi = \frac{\mathbf{\Pi}^2}{2m}+e\phi$$
...
12
votes
1
answer
453
views
Is the uniqueness theorem correct in superconductivity?
There is an uniqueness theorem in electromagnetism. It says that the solution of Maxwell's Equations is determined uniquely by boundary conditions.
We can treat superconductivity as a completely ...
11
votes
3
answers
2k
views
Propagator of Maxwell-Chern-Simons theory
I need to compute the "topologically massive photon" propagator.
I've started with:
$$
\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \frac{\mu}{4}\epsilon^{\mu\nu\lambda}A_\mu\partial_\nu ...
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-...
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 $r_0<r<R$ ...
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 ...
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?
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}}{...
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 ...
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 ...
8
votes
1
answer
5k
views
The gauge-invariance of the probability current
It is simple to show that under the gauge transformation $$\begin{cases}\vec A\to\vec A+\nabla\chi\\
\phi\to\phi-\frac{\partial \chi}{\partial t}\\
\psi\to \psi \exp\left(\frac{iq\chi}{\hbar}\right)\...
8
votes
1
answer
406
views
Quantum Cyclotron Frequency - Why is it off by a factor of 2?
Say you have a magnetic field $\vec{B}=(0,0,B_0)$. Then the Schrodinger Equation Hamiltonian for a spin-2 particle of charge $e$ moving in this field is:
$$H = \frac{1}{2m}[\vec{p}-e\vec{A}]^2-\vec{\...
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,...
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 ...
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^...
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 ...
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 ...
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 ...
6
votes
2
answers
1k
views
Dirac Delta Magnetic field
Suppose, we are given a magnetic field $\vec{B}$ as:
$$\vec{B} = \phi \delta(x)\delta(y)\hat{e}_z$$
where $\phi$ is some constant and $\delta$ is dirac delta function.
How do we find the corresponding ...
6
votes
4
answers
8k
views
How do we deduce the vector potential for a constant magnetic field?
How do we show that for a constant magnetic field $\vec B = const$, the vector potential is $\vec A = \frac12 \vec r \times \vec B$?
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 ...
6
votes
3
answers
6k
views
Is this a Lorentz-scalar? How do I tell?
I'm struggling to identify whether a scalar is a Lorentz-scalar. E.g:
$$\partial_i A^i \quad i \in {1,2,3}.$$
How do I determine if this is a Lorentz-scalar or not?
If got the same problem with ...
6
votes
2
answers
2k
views
Derivation of Ampere's Law in Jackson
The derivation of Ampere's Law in Jackson E&M from the Biot Savart law is for the most part fairly traditional, using the $\nabla\times(\nabla\times A)$ identity on the vector potential:
$$\nabla\...
6
votes
2
answers
7k
views
Pressure experienced due to magnetic force?
A current $I$ flows in a long thin walled cylinder(parallel to the axis) of radius $R$. What pressure do the walls experience?
This is the 263rd problem in Section III from the book 'Problems In ...
6
votes
3
answers
1k
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Physics olympiad question about a charge capacitor
This is problem 1463 from the Russian magazine Quant.
Unfortunately my Russian is not good enough, so I apologize if the translation of the problem contains errors.
Problem. Inside a flat charge ...
6
votes
2
answers
413
views
Induced current using a reference system bound with a moving charge
Suppose we have a charge moving at velocity $\mathbf{v}$ in the same plane of a square wire.
If I sit in a reference frame where the square wire is still, since the charge is moving with velocity $...
6
votes
3
answers
1k
views
What would it take to cause lightning to jump between the Moon and the Earth?
This question comes from @Floris' speculation at the end of his excellent answer about what it would take to kill everyone on the Earth with electricity.
Doing all this in 1/10th of a second requires ...
6
votes
1
answer
6k
views
Calculating the electrostatic energy per unit length of a cylindrical shell surrounded by a coaxial cable
Suppose an infinitely long cylindrical shell of radius $a$ carries a surface charge density $\sigma_0$ and is surrounded by a coaxial cable of inner radius $b$ and outer radius $c$ with uniform charge ...
6
votes
2
answers
2k
views
Can we explicitly solve the Hamilton–Jacobi equation for a particle in a uniform magnetic field?
HJE for nonrelativistic charged particle in an electromagnetic field is
$$\frac{1}{2m}\left(\nabla S - q\mathbf{A}\right)^2 + q\phi + \frac{\partial S}{\partial t} = 0.$$
For a uniform magnetic ...
6
votes
0
answers
1k
views
Why is there no induced current in this loop? [closed]
This problem comes from Barron's SAT Subject Test Physics book.
A loop of wire and a bar magnet are moving relative to one another. Which motion in the diagrams shown below will NOT induce a ...
5
votes
3
answers
666
views
How to see $\mathbf{E}\cdot\mathbf{B}$ is a total derivative?
Since $\mathbf{E}\cdot\mathbf{B}$ is a Lorentz invariant of the electromagnetic fields it seems like an interesting thing to plug into a Lagrangian to see what happens. However, this ends up ...
5
votes
1
answer
545
views
Why do planets not radiate EM waves in their orbits?
Despite being overall near-netural, I would expect the individual electrons and proton to radiate long EM waves as we accelerate around the Sun or rotate around our poles. Is the acceleration so small ...
5
votes
2
answers
11k
views
Equivalent form of Bianchi identity in electromagnetism
In electromagnetism, we can write the Bianchi identity in terms of the field strength tensor $F_{\mu \nu}$ as,
$$ \partial_{\lambda} F_{\mu \nu} + \partial_{\mu} F_{\nu \lambda}+ \partial_{\nu} F_{\...
5
votes
3
answers
3k
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Energy-Momentum Tensor for Electromagnetism in Curved Space
$\newcommand{\l}{\mathcal L} \newcommand{\g}{\sqrt{-g}}$$\newcommand{\fdv}[2]{\frac{\delta #1}{\delta #2}}$I want to calculate the energy-momentum tensor in curved free space by functional ...
5
votes
2
answers
4k
views
Make a semi transparent mirror with copper
The question:
How would you make a semi transparent mirror (50% reflection, 50% transmission) with glass with a layer of copper. For light $\lambda$ = 500nm Try to be as realistic as possible
What I'...
5
votes
2
answers
2k
views
Rotating bar magnet : current induced in circuit
I don't think this problem makes sense. The answer given is (a). Aren't the field lines parallel to the loop, what does rotation affect ? create atomic currents?
5
votes
2
answers
3k
views
Derivative of the electromagnetic tensor invariant $F_{\mu\nu}F^{\mu\nu}$
The electromagnetic field tensor is $F_{\mu\nu}=\partial_\mu A_\nu - \partial_\nu A_\mu$. I am trying to calculate the quantity
$$ \frac{\partial(F_{\alpha\beta}F^{\alpha\beta})}{\partial(\partial_{\...