8
votes
Accepted
Two permanent magnets are allowed to attract each other. The field energy MUST decrease as they speed up. But Griffiths implies it INCREASES. How?
The system that Griffiths describes here makes heavy use of static phenomena (static magnetic fields , generated by a constant current). Strictly speaking they are only valid when the velocity of the ...
- 5,986
6
votes
Accepted
Low temperature behavior for ferromagnets: theoretical and experimental discrepancies
Start from the definition of $\tanh x$ in terms of exponentials
\begin{align}
\tanh x &= \frac{e^x -e^{-x}}{e^x +e^{-x}}\\
&= \frac{1 - e^{-2x}}{1 + e^{-2x}}\\
&=(1 - e^{-2x})\left(1 - e^{-...
- 8,022
5
votes
Low temperature behavior for ferromagnets: theoretical and experimental discrepancies
For the first question you can rewrite $\tanh$ in terms of exponentials, see e.g. this Math.SE post for details. For the second question, yes, $M(0)$ is the magnetization in the zero temperature limit,...
- 2,108
4
votes
Accepted
Does Number of turns matter?
Your notation is not standard (edit: at least it was not standard before your edit). $N$ is ordinarily considered to be the number of turns, and $n=\frac N l$ is the number of turns per unit length. ...
- 1,128
3
votes
Deriving transformation property of $\vec{E}$ and $\vec{B}$ under Galilean transformation
Accelerations are invariant under Galilean transformations, therefore forces are invariant under Galilean transformations. Full stop. If it's a force, it's invariant. It doesn't matter what the force ...
- 21.3k
3
votes
Is force perpendicular to magnetic field in a bar magnet?
If you look at extremely old high school books (say a high school textbook from the US in the 1920's, like Millikan), it's fairly common to see this style of presentation. However, it's extremely ...
- 31
2
votes
Accepted
Why are sunspots cooler than the other regions?
As I discuss in https://physics.stackexchange.com/a/415248/59023 and https://physics.stackexchange.com/a/708183/59023, a sunspot is a pressure-balance structure. The total pressure in a collisionally ...
- 14.7k
2
votes
Accepted
What is rotation of magnetization?
One can think of a domain as a region where many atoms line up so that the magnetic field they produce add together to produce a resultant magnetic field.
Imagine that magnetic field as being produced ...
- 81k
2
votes
What type of electric field is created by time varying magnetic field?
Yes, the electric field $\mathbf{E}$ induced by a time-varying
magnetic field $\mathbf{B}$ is according to Faraday's law of induction
$$\mathbf{\nabla}\times\mathbf{E}=- \frac{\partial\mathbf{B}}{\...
- 28.3k
2
votes
Deriving transformation property of $\vec{E}$ and $\vec{B}$ under Galilean transformation
Look for $v/c \sim 0$ of the transformations, as an example non-relativistic approximation in wiki: https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity.
You can start with ...
- 2,318
1
vote
Can trains use permanent magnets to be propelled?
Permanent magnets might allow you to furnish the levitation force needed to lift the train out of contact with the rails, but because they are permanent there is no way to switch them on and off and ...
- 76.7k
1
vote
Deriving transformation property of $\vec{E}$ and $\vec{B}$ under Galilean transformation
I'm going to take a step back and start with a more basic question: "what does it mean to ask how a field transforms?"
This is the answer I would give to that question:
Say we set up some ...
- 36.3k
1
vote
Accepted
Relative permeability: why does $\mu_{air} = \mu_0$?
Ferromagnetic materials can have large $\mu$. But for paramagnetic and diamagnetic materials, a typical permeability is
$
\mu_r = \frac{\mu}{\mu_0} ≈ 1 \pm 10^{-5}
$.
I don’t know of a good ...
rob♦
- 75.9k
1
vote
Does Number of turns matter?
Yes, that's right, magnetic flux density $\mathbf{B}$ is proportional to the number of turns per unit length. If a source says $\mathbf{B}$ is proportional to the number of turns, then they are ...
- 31
1
vote
Proving induced voltages will always cancel in circuit that is in a $B$-field
The induced voltage will definitely not cancel in general. That is the entire point of magnetic induction. Unless you specify that the field is constant and the wires don't move, it is actually quite ...
- 514
1
vote
Accepted
Understanding why the current can be treated like below for magentic field calculation
The usual Biot-Savart law looks like
Where we can set vector $\vec{e}=\vec{dl}/|\vec{dl}|$ in the current direction. So, if cross-sectional area of wire is S we can rewrite:
$$\vec{B}(\vec{r})=\dfrac{...
- 471
1
vote
Accepted
Is MRI permanent magnet sensitive to temperature?
Yes. Most MRI systems use superconducting electro magnets rather than permanent magnets for this reason (among others). However, for the MRI systems that do use permanent magnets, one of their major ...
- 71.4k
1
vote
Classical Harmonic Oscillator in a Magnetic Field
This is a system of linear differential equations with constant coefficients, which can be solved by many approaches. Perhaps, it is worth pointing out that, since the order of the system is $4$, one ...
- 42.5k
1
vote
Classical Harmonic Oscillator in a Magnetic Field
To decouple your equations, you can perform the change of variable
$$z=x+iy$$
so that
$$m\ddot z=kz-ia\dot z$$
Solutions are exponential, $z=e^{rt}$ with $mr^2=k-iar$. Finally, $x$ and $y$ are given ...
- 2,432
1
vote
What type of electric field is created by time varying magnetic field?
The electric field in the potential formulation takes the form:
$$\vec{E} = -\nabla V - \frac{\partial\vec{A}}{\partial t}$$
In the coulomb gauge;
The term $-\nabla V$ is purely divergent. ie - is ...
- 5,325
1
vote
Accepted
What is the multiplicity of a microstate (not macrostate!)
Almost certainly the multiplicity of a microstate means the number of microstates that are contained within the macrostate that contains the given microstate (and so is the same as the multiplicity of ...
- 36.9k
1
vote
Accepted
Thermodynamic relation $p$ for a paramagnetic system
Most generally, we can write for any closed (constant-$N$) system the expressions
$$dU=\delta Q+\delta W;$$
$$dU=T\,dS+\sum_j X_j\,dY_j;$$
that is, we can increase the energy $U$ through heating ($\...
- 15.6k
1
vote
What happens to the energy in the magnetic field of a ferromagnet when it is heated past its Curie Temperature?
The reduction in the magnetic field within the magnet would be accompanied by eddy currents, in accordance with Faraday's law (EMF driving the current is $\varepsilon = -\frac{d}{dt} \int_{\Sigma}{\...
- 804
1
vote
What happens to the energy in the magnetic field of a ferromagnet when it is heated past its Curie Temperature?
Well, if you take a "proper" second-order ferromagnet-paramagnet phase transition (which happens to be the case for pure iron), then the magnetization does not disappear suddenly. It is a ...
- 580
1
vote
Doubling the length of a solenoid doubles its inductance. Two identical solenoids in series have up to four times the inductance due to M. Why?
But this case is identical to the first case where we simply doubled the length of the original inductor and doubled the number of turns to get $L_{new}=2L_0$ so we have a contradiction. How can this ...
- 42.5k
1
vote
Accepted
Use of soft iron in electromagnets despite having very high retentivity
Soft iron is commonly used here because it is easily magnetized, easy to machine, and cheap.
For an AC motor, the magnetic field direction is flipping constantly, so there is no chance of building up ...
- 76.7k
1
vote
Accepted
Is force perpendicular to magnetic field in a bar magnet?
$\mathbf F$ and $\mathbf B$ are indeed in the same direction. Remember that in the equation you quote the (imaginary) thing on which the force acts is not a moving charge but a (North) monopole.
Think ...
- 29.2k
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