Questions tagged [magnetostatics]

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3answers
235 views

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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3answers
233 views

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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1answer
53 views

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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2answers
51 views

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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2answers
119 views

Direction of Integration in Biot Savart's Law (Line Integral)

Let's say we have a loop with a clockwise current, and my angle increases in the counter-clockwise direction (that is, $\hat{\phi}$ is counter-clockwise). I have $$B=\frac{\mu_{0} i\vec{dl} \times \...
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1answer
50 views

Intuitively, why is the net current through a volume $0$ if the current is steady?

Say I want to find the total current passing through the following volume, provided by Griffiths' textbook on Electromagnetism. It's not the most useful image, but perhaps imagine the inner curved ...
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1answer
43 views

Magnetic field and magnet [duplicate]

We know that magnetic does not do any physical work . Now consider; we attached a magnet in a wall with help of a tape. Now we bring a magnet near to other magnet and released we see that magnet will ...
0
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1answer
126 views

How to use Ampere's law for a semi-infinite current sheet?

I have a very thin current sheet with constant current density K in the y-direction, length w in the x-direction, and infinitely long in the y-direction. I have to find an expressions for the magnetic ...
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0answers
40 views

Doubt on why magnetic flux density is solenoidal

The $\mathbf{H}$ field can be derived from the potential $\psi$: $$\mathbf{H}=\dfrac{\mu_0}{4 \pi} \int_{V'} \rho \dfrac{\mathbf{r}-\mathbf{r'}}{|\mathbf{r}-\mathbf{r'}|^3} dV' + \dfrac{\mu_0}{4 \pi}...
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1answer
42 views

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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1answer
74 views

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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0answers
21 views

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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2answers
64 views

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 ...
7
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1answer
181 views

On the applicability of Coulomb's law and the Biot-Savart law

Jefimenko's equations are $$\textbf{E}(\textbf{r}, t_r) = \frac{1}{4\pi\epsilon_0}\int \left[\rho\left(\textbf{r}', t_r\right)\frac{\textbf{r} - \textbf{r}'}{\left|\textbf{r} - \textbf{r}'\right|^3} + ...
2
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1answer
64 views

Can I replace a multipole expansion by a combination of separate dipoles?

If I want to be able to model a magnetic field flux density $\mathbf{B}$ from a magnetic source located at the origin at a position $\mathbf{r}$, it is my understanding that I can represent $\mathbf{B}...
2
votes
2answers
225 views

Magnetic levitation against Earnshaw's Theorem?

Given six strong magnets, what if we fix three of them to a table in a simple, horizontal, equilateral triangle-like formation (with their north poles sticking up), and the other three to the points ...
5
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1answer
135 views

Deduction of $\mathbf H =\dfrac{\mathbf B}{\mu_0}-\mathbf M$

merry Christmas to all the users! I want to get to $\mathbf H =\dfrac{\mathbf B}{\mu_0}-\mathbf M$ from the superposition principle, like some texts have done in electrostatics with $\mathbf D=\...
1
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1answer
85 views

What is Magnetic Intensity? [duplicate]

While studying about the magnetic properties of matter, my book defines this vector as $\vec{H}=\dfrac{\vec{B}}{\mu_0}-\vec{M}$ where $B$ is the magnetic field and $M$ is the intensity of ...
2
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1answer
196 views

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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2answers
541 views

What are the possible magnetic fields with constant magnitude?

A now-deleted answer to this recent question prompted me to wonder about this and I can't find a clear answer in the top layer of google results, so I thought I'd ask here. What are the possible ...
0
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1answer
107 views

Curl of magnetic field produced by current carrying wires with infinitesimal small area

Can Magnetic fields produced by thin current carrying wires with infinitesimal area have curl with a delta function in it ?? As area is Zero current density J definitely becomes infinite at where ...
4
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1answer
128 views

Equation for the field of a magnetic dipole

In my electrodynamics class, my professor derived the equation for the field of the magnetic dipole $$\vec{B}(\vec{r})=\frac{\mu_0}{4\pi}\frac{1}{r^3}[3(\vec{m}\cdot\hat{r})\hat{r}-\vec{m}]+\frac{2\...
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1answer
52 views

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 ...
5
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1answer
188 views

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 "...
4
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1answer
324 views

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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1answer
135 views

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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1answer
45 views

Static Electromagnetic fiels [closed]

What is the mathematical proof that static electric and magnetic fields are independent of each other?
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1answer
97 views

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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1answer
66 views

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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0answers
70 views

How to calculate the magnetic field of two cylinders when one of them is rotating

Given is the voltage U and the Angular velocity $\omega$. The rotating cylinder is inside the other cylinder and U is measured between them. To calculate the magnetic field, I tried to solve $\oint ...
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1answer
102 views

How did scientists before Coulomb ensured this fundamental property of magnets? [closed]

Firstly, please note that I am talking about the period BEFORE electricity and magnetism were unified. So I am NOT seeking for answers based on Ampere atomic current model of magnets. I have read the ...
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2answers
77 views

What exactly is meant by magnetic poles?

If I have a magnet, which of the following is really called magnetic pole and why?: $(1)$ Half of the volume of the magnet - north pole, other half volume - south pole. $(2)$ Area at one end of the ...
1
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1answer
58 views

Demagnetising $H$ field

If we have a permanent magnet we know that we have a $H$ field opposite in direction to the residual magnetic field $B_r$. The $H$ field causes a demagnetisation, but how does it do it? We know that ...
1
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1answer
182 views

Help understanding Biot-Savart Law

In the Biot Savart law, it's my understanding that dL represents an infinitesimally small length of the wire carrying current. See below. However, I ran into a practice problem that is confusing me. ...
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1answer
89 views

Electromagnetic Wave (Without Magnetic and Electric Field)

As I know, every electromagnetic wave has magnetic and electric field component (perpendicular to the direction of wave). I have a doubt about this, as a hot iron bar also emits EM waves, and as ...
0
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2answers
174 views

Field Lines of a Bar Magnet

I'm trying to plot magnetic field lines for a rectangular bar magnet in 3 dimensional space. The position of the magnet is known and we wish to produce a plot such as the one shown below. Can ...
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4answers
244 views

Analogue of charge distribution in magnetostatics

Short of magnetic monopoles, what is the analogue of charge distribution in magnetostatics? Can we call it magnetic pole distribution?
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0answers
94 views

Boundary conditions in the method of images

My question is very similar to this one. The problem: A long thin wire carrying a current $I$ lies parallel to and at a distance d from a semiinfinite slab of iron. Assuming the iron to have infinite ...
-1
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1answer
254 views

Magnetic field of magnetic dipole along the z-axis

The vector potential for a magnetic dipole is given by the following formula: $$ \vec{A} = \frac{1}{4\pi\epsilon_0 c^2}\frac{\vec{m}\times\hat{e}}{R^2} $$ From this expression we can deduce that for ...
1
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1answer
140 views

Magnetic field inside a perfectly diamagnetic ball

I am quite confused about this. Imagine we put a perfectly diamagnetic sphere in homogenuous magnetic field $$ \vec{B} = B_0 \, \vec{e}_z $$ You can verify yourself that the solution outside the ...
-1
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1answer
187 views

Why do we consider a circle as a closed loop while deriving the magnetic field of a infinitely long wire [closed]

Why do we consider a circle as a closed loop while deriving the magnetic field of a infinitely long wire. How does it affect if I take another shape.
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1answer
1k views

Obtaining the magnetic vector potential inside an infinite cylinder carrying a z directed current:

Suppose we have a nonmagnetic conducting cylinder of radius $ \alpha $ directed in the z direction, with a current density $ J_{0} \hat{a_{z}} $. What is the magnetic vector potential for $\rho < \...
4
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0answers
74 views

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?
1
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1answer
77 views

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 ...
1
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1answer
2k views

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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1answer
118 views

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 ...
1
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1answer
44 views

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 ...
2
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6answers
859 views

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{\...
2
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0answers
178 views

Diamagnetic materials with negative susceptibility?

I have been learning about magnetostatics, and from reading about the existence of diamagnetic, paramagnetic and ferromagnetic materials I was under the impression that a limiting value for magnetic ...
1
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0answers
606 views

Surface current density (magnetic materials)

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 ...