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Questions tagged [magnetostatics]

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Detecting if there was a repulsion or attraction on a magnet

I would like to know if we have a way of detecting if a magnet reacts to a iron bar or attract /repel by another magnet. Would be able to see through a sensor if there was some activity in the ...
1
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1answer
36 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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0answers
8 views

Looking for ways to transform time-series data recorded from object movement into equation describing the movement direction of the object

Looking for some time-series data transformation advice! I want to know what's the best way to transform data of 9-tuples time series data of IMU (Inertia Measurement Unit) sensor, recorded from a ...
1
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2answers
43 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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0answers
31 views

Please clarify a doubt in the article: Reflections in Maxwell's treatise

While going through an article titled "Reflections in Maxwell's treatise" a misunderstanding popped out at page 227 and 228. Consider the following equations $(23\ a)$ and $(23\ c)$ in the article (...
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2answers
38 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
27 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
34 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 ...
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1answer
29 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
36 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
37 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
43 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
16 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
59 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 ...
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1answer
161 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} + ...
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1answer
51 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
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2answers
118 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 tree to the points of ...
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1answer
104 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=\...
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1answer
39 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
130 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
483 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 ...
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1answer
70 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 ...
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1answer
75 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
46 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 ...
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1answer
135 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
213 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
78 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 ...
0
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1answer
43 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
49 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
38 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
59 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 ...
0
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1answer
98 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
60 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 ...
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1answer
43 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
107 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. ...
0
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1answer
76 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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1answer
82 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
90 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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48 views

On the derivation of the magnetic part of the Lorentz force

I'm reading the book "Grundkurs Theoretische Physik 3; Elektrodynmaik" by Nolting. In chapter 3.2.1 he derives the magnetic part of the Lorentz force$$F=q\textbf{v}\left(\textbf{r}_o\right)\times \...
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0answers
40 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 ...
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1answer
137 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 ...
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1answer
84 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 ...
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1answer
112 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.
0
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1answer
700 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 < \...
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0answers
54 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?
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1answer
70 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 ...
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1answer
848 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
84 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 ...
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1answer
40 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 ...
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6answers
697 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{\...