# Questions tagged [magnetostatics]

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### Curl of magnetic field (Ampère's law)

I'm a little bit confused about Ampère's law concerning the curl of a magnetic field: $$\vec{\nabla}\times\vec{B}(\vec{r}) = \mu_{0}\vec{J}(\vec{r})$$ with $\vec{J}(\vec{r})$ the volume current ...
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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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### Magnetic Field Energy Increase while magnetic field does work on a current carrying loop - Where does the energy come from?

Imagine you have an external magnetic Field $\vec{B}_{\text{ext}}$(for the sake of simplicity, it should be constant throughout the entire space), which is not generated by any current density (...
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### Is there a force between current-carrying parallel wires when the charges move with the same, constant velocity in each?

Let's assume that all charges flowing in both wires are either all positive or all negative. From the frame of reference of an individual charge in either wire, it would appear as if the position of ...
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### Confusion regarding torque given by M×B

The magnetic torque acting on a loop of magnetic moment M placed in a magnetic field B, is given by τ=M×B. My question is, about which axis does this give the torque about? Is it the instantaneous ...
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### How is it possible that one face of my electromagnet produces stronger magnetic field than the other?

I work in an experimental research lab. I made an electromagnet by having the machine shop cut through a toroid core and hand-winding wire around it. The objective is to have a region of uniform ...
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### Similarities and analogies between the $E, P$ and $D$ fields with the $B, M$ and $H$ fields and their limitations

In the course of my learning electromagnetism, I’ve noticed there are a striking amount of symmetries in electrostatics and magnetostatics, almost down to replacing divergence operators with curl ...
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### How is energy conserved in this case?

Consider a permanent magnet introducing a magnetic field at some fixed angle to a loop of wire on a spindle. If a fixed current is allowed to run through the wire, the lorentz force introduces a net ...
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### How is the third case obeying integral form of Maxwell's second equation?

Let $m$ denote pole strength. In the diagrams: (1) Sky blue: Closed Gaussian surface (2) Red: North pole of magnet (3) Green: South pole of magnet (4) Yellow: Part of magnet cutting Gaussian surface ...
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### Question about the definition of magnetostatics

From my understanding, magnetostatics is defined to be the regime in which the magnetic field is constant in time. However, Griffiths defines magnetostatics to be the regime in which currents are "...
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### When does $\nabla \times B =0$?

In my lab, I use electromagnets to apply a magnetic gradient force to lots of very small (superparamagnetic) nanoparticles embedded in an elastic medium. I believe that these can be treated as ...
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### Magnetization of spherical aluminum shell? [closed]

Consider a hollow aluminum sphere (assume 1 cm diameter, 1 mm wall thickness, filled with and surrounded by air) placed in a uniform magnetic field (assume 10-20 mT). Are there any realistic ...
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### Static Electromagnetic fiels [closed]

What is the mathematical proof that static electric and magnetic fields are independent of each other?
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### Confusion in deriving Gauss law for magnetism

I am deriving Gauss law for magnetism from Coulomb's law of magnetic poles. I have a cubical magnet as shown below and the Gaussian surface is inside the magnet: The magnet can be considered as a ...
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### Is the equation $\vec{B}=\mu\vec{H}$ correct in general? How shall we derive it?

The relation between magnetic flux density $(\vec{B})$ and magnetic field intensity $(\vec{H})$, in general, is: \begin{equation} \vec{B}=\mu_0(\vec{H}+\vec{M}) \tag{1} \end{equation} One of my ...
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### Work done by a magnetostatic field [duplicate]

How does a (static) magnetic field accelerate objects (like an iron nail) if we are taught that the magnetic force does always zero work?
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### Force without magnetic or electric field

In a long primary solenoid,if we introduce a secondary one on its outer surface,due to mutual inductance-an emf is generated in the secondary one according to Lenz's law if there is a time varying ...
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### Deriving Ampere's law from Biot-Savart equation [closed]

As an exercise, I've been trying to derive Ampere's law from the Biot-Savart equation (in the static case). So basically I'm trying to prove: \begin{equation} \nabla \times \vec{B}(\vec{r}) = \mu_0\...
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### Consider three infinitely long thin wires [closed]

Each carrying current I in the same direction , are in $x$-$y$ plane. The central wire is along the $y$ axis, while the other along $x=+d$ and $-d$ Find the locus of points for which magnetic field ...
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### What is a minimal set of quantities fully describing the source of a magnetic field?

Assume I would like to compare different magnetic fields without knowing what generates them. What is the minimal set of physical properties describing a field that would let me calculate all the ...
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### Forms of Maxwell's equations

In my physics class, I was taught two forms of one of Maxwell's equations: Ampere's law $$\vec{\nabla} \times \vec{B} = \mu J$$ and Maxwell-Ampere's law c^2\vec{\nabla} \times \vec{B} = \dfrac{\...
In deriving the boundary conditions for $H$ at the boundary between two media, my lecturer stated that "since there is no conduction (free) current on the Surface... the tangential components of H are ...