# Questions tagged [magnetostatics]

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### Magnetic scalar potential far above a magnetic film

The situation I am looking at is a magneto-static problem of a finite magnetic film with magnetization $\bf{M}$. I would like to find the the magnetic field far above the plate. My expectation is that ...
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### Is Biot-Savart Law valid for time-varying currents unlike Ampere's law?

I have just finished learning the basics of magnetism, and it should be noted that I am not very familiar with Maxwell's equations. Note: In the question, when I say "Ampere's Law", I am referring ...
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### Are there cases where $\nabla\cdot\iiint\frac{\mathbf{J}(\mathbf{x}')}{\left|\mathbf{x}-\mathbf{x'}\right|}\mathrm{d}V' \neq 0$?

In Jackson's Classical Electrodynamics, Section 5.4 (Vector Potential), the author seems to assume that because $\nabla\cdot\mathbf{J} = 0$, the following holds for the current density (where the ...
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### For a constant magnetic field, is there a gauge with both canonical momenta conserved?

To describe a constant magnetic field $\mathbf B=(0,0,B)$ (ignoring the motion along the $z$ dimension) within hamiltonian (or quantum) mechanics, one needs to choose a gauge. One common gauge is the ...
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### What is the importance of vector potential not being unique?

For a magnetic field we can have different solutions of its vector potential. What is the physical aspect of this fact? I mean, why the nature allows us not to have an unique vector potential of a ...
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### Current geometry and Ampere's law

Under the right circumstances, Ampere's law $\oint \vec H\cdot d\vec \ell=I_{encl}$ can be used to deduce the field $\vec H$ at a point from the current enclosed by the circuit which produces $\vec H$....
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### Solution of simple problems using only Maxwell equations in differential form

Solve simple electrostatic or magnetostatic problems using only Maxwell equations. For example: In every book there is an excercise to find a magnetic field outside a thin wire of radius $a$ with ...
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### What determines whether we use a vector or scalar potential?

I understand that electrostatic potential is scalar because the curl of the field is zero, and this implies the electrostatic field is the gradient of the scalar potential to satisfy this. Similarly ...
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### Ampère's law applied on a “short” current-carrying wire

Why doesn't Ampère's law hold for short current carrying wires? Of course, such wires should be part of a closed circuit, but that's a physical fact, and there is a numerous amount of ways to close it....
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### How does the magnetic field generated from a rectangular cross-sectional current-carrying conductor differ from a circular cross-sectional conductor?

I can find much information of cylindrical conductors (ie. regular wires), where $B=\frac{\mu_0 i}{2 \pi r}$ and $r$ represents the radius (or distance) from the centre of the conductor, however I ...
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### What is the physical basis of the $\rho \bf{u} \times \bf{\omega}$ force on a fluid vortex line?

In fluid dynamics, the force density on a vortex line is $\bf{f} = \rho \bf{u} \times \bf{\omega}$. In Faber, Fluid Dynamics for Physicists, ch. 4, this is "derived" by analogy with magnetostatics, ...
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### Frozen in Magnetic Field Lines

A perfectly conducting fluid undergoes an axisymmetric motion and contains an azimuthal magnetic field $\textbf{B}_θ$ . Show that $\dfrac{B_θ}{r}$ is conserved by each fluid element. Question from ...
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### Can the magnetic force between two magnets be explained classically via magnetization current?

Usually in Electrodynamics courses the magnetic forces are analysed via wire-wire interaction. I don't remember being shown a classical explanation for magnetic forces between magnets. Since it is a ...
I am trying to determine if the following problem has an analytical solution using the method of images. The problem is an infinitely long (in $z$) cylinder of a material with permeability $\mu_2$ of ...