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Questions tagged [magnetostatics]

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Determine the torque of a rotating cylinder [closed]

I'm working on a homework assignment and seem to be stuck. The question is as follows: I started off by calculating the magnetic dipole moment of the cylinder first and ended up with something ...
8
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1answer
156 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
50 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}...
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2answers
92 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 ...
5
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1answer
99 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
33 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
69 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
459 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
43 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
67 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
125 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 "...
5
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1answer
194 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
58 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
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
40 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
52 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
95 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
58 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
39 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 ...
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1answer
66 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
69 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 ...
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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
62 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
43 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
34 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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0answers
155 views

Magnetic field created by single charge and racing electrons

Imagine a single charge moving at a certain linear speed in a circular path, just like the ring below. Does it create a static magnetic field just like the one on the image below, only a lot weaker? ...
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0answers
113 views

Boundary conditions of magnetic fields in matter

I'm currently reading Griffith's "Introduction to electrodynamics". I have a doubt on boundary conditions for magnetic fields in matter. It has been treated before that when $\vec{B}$ crosses a ...
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1answer
111 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
62 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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0answers
52 views

Why do some protons line up the wrong way in a strong magnetic field?

The discussion of MRI scanning in my physics book says: Most [protons] line up with their N poles facing the S pole of the [strong] external [magnetic] field, a few line up the other way round, ...
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1answer
89 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
559 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
52 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
68 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
688 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
75 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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0answers
184 views

Magnetic field of a current carrying wire

I have 2 questions about the geometry of magnetic fields. Suppose a steady current flows in a square loop. This current will generate a uniform magnetic field. How does the magnetic field produced by ...
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6answers
619 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{\...
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0answers
99 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 ...
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0answers
348 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 ...
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1answer
394 views

Lorentz force law and Ampère's force law

The Lorentz force law specifies the force of a magnetic field on a moving charged particle, and the Ampere force law specifies the force of a magnetic field on a current carrying wire. I am trying to ...
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1answer
64 views

Are there any south and north poles developed when we flow electric current through a Toroidal Solenoid?

I've read that when current flows in a solenoid it behaves like a bar magnet having both north and south poles. I was wondering how can we visualise north and south poles in a **Toroidal Solenoid".
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1answer
53 views

Why am I getting two different results in emu and SI unit?

I am computing force between two magnetic poles each of one unit pole (in emu) and situated one centimeter apart. In electromagnetic units: $$F_{dyne}=\dfrac{p^2}{r_{cm}^2}=\dfrac{1^2}{1^2}=1 dyne$$ ...
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1answer
54 views

Direction of magnetic field clarification

For a circular wire carrying current $I$ in the counterclockwise direction (in the xy-plane), the magnetic field points in the positive $z$ direction. I tried to understand this more by drawing out ...
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1answer
78 views

Magnetic potential and magnetic field assumptions

I've seen many proofs where you want to find the magnetic field inside and outside a solenoid for example. The author said using symmetry magnetic potential is a function of some variables and discard ...
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2answers
707 views

Magnetic flux through current loop

I am trying to calculate the total magnetic flux through the surface of a current loop. I feel that this flux should be finite and nonzero -- so far any attempt in calculating failed. Can this really ...
4
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1answer
580 views

What is the correct expression for the magnetic energy density inside matter?

I'll use a magnetized sphere as an example, of radius $R$, with a magnetization density $\vec{M}$. The magnetic moment of the sphere is $\vec{\mu} = \vec{M} \, V$. The magnetic field inside and ...