# Tag Info

## Hot answers tagged magnetic-fields

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 ...
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### 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^{-...
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### 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,...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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