Questions tagged [magnetostatics]

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Derivation of Ampere's Law in Jackson

The derivation of Ampere's Law in Jackson E&M from the Biot Savart law is for the most part fairly traditional, using the $\nabla\times(\nabla\times A)$ identity on the vector potential: $$\nabla\...
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1answer
458 views

Magnetization and magnetic moment

If a current carrying loop has magnetic moment m, how can i determine the magnetization M, of it? Ive done some reading and have found a formula that seems to solve it, it says that M is equal to the ...
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1answer
59 views

When to apply $\frac{mv^2}{r} = q .v .B$

A charged particle of mass $m$ is moving with a speed $u$ in a circle of radius $r$ . If the magnetic field induction at the centre is $B$ and the charge on particle is $q$. I want to know why I can't ...
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1answer
647 views

Relationship between current and magnetism [closed]

If 2 pieces of iron are next to each other, there is no magnetic attraction. However if a current is run through them, they will behave as magnets. My question is is there a relationship between the ...
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1answer
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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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1answer
109 views

Why is the magnetic unit twice the electric one in CGS?

In CGS system the electric unit is the esu or statcoulomb equal to $2.08*10^9$ charges and two such units repel with a force of $1$ dyne. Magnetic force ratio is $v^2/c^2$, therefore the magnetic ...
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1answer
3k views

Magnetic force on a charged particle doesn't affect total energy

So there's this sentence in a book I am reading. It states "When a charged particle is placed within a magnetic field, despite the magnetic force acting on the particle, there will be no change in the ...
2
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1answer
270 views

Magnetic field interaction energy term

I am trying to derive the Ginzburg-Landau free energy for superconductors, and I follow most of it apart from the introduction on the term containing the magnetic field. This is the bit I don't ...
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0answers
80 views

Net magnetic field & magnetization on a ferromagnetic material

A ferromagnetic materiel is saturated by an exterior magnetic field like so: Where $B_1$ is a uniform magnetic field. Then after some time $t$ another magnetic field $B_2$ is introduced as well, but ...
5
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1answer
2k views

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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0answers
301 views

When do we have a coherent magnetization rotation? (single-domain particles)

So I am studying micromagnetics + spintronics and I am little bit confused with certain concepts regarding the physics of magnetic domains (especially single domain particles): What I already knew: ...
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2answers
381 views

Deflection of compass and rest position through Magnetic induction

I found a problem with a compass and a magnet, as diagrammed below. The needle of the compass was oscillating, but when a soft iron bar was placed in the “X” then the needle came to rest. Why did ...
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2answers
255 views

What causes the pattern you see when you hold a strong magnet near a CRT TV?

When you hold a powerful magnet near an old-style CRT TV, you see an interesting pattern, which "shows up the field lines" (see https://www.youtube.com/watch?v=_yEu2R1gYSs&feature=youtu.be&t=...
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2answers
1k views

How can we apply Ampère's circuital law in a wire?

How can we apply Ampere's circuital law in a wire to calculate magnetic field around a straight current carrying wire? The length of the wire is not infinite. Using the Biot-Savart law we get $$B = ...
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0answers
320 views

Are these magnetic field lines drawn correctly? [closed]

I was asked to reason out if the following magnetic field lines are correctly described or not. (A) (The blue line is a solenoid and the dark ones are the field lines) My answer:I think these are ...
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2answers
785 views

What does it mean to be unique in terms of vector potentials?

I was in an electromagnetism lecture, where we were looking at the magnetostatic Maxwell’s equations: $$\begin{align} \nabla\cdot\mathbf{B} &= 0 \\ \nabla\times\mathbf{B} &= \mu_0\mathbf{J} \...
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1answer
477 views

Ferromagnets - Permanent?

When researching about the Curie-Temperature and magnets in general, something got me confused. What is the difference between a ferromagnet and a permanent magnet? In a ferromagnet the spins are ...
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0answers
267 views

Circularly Magnetized Neodymium Torus With Minimum Flux Leakage

I'd like to conduct some experiments related to Aharonov-Bohm. In particular, I'd like to investigate the irrotational vector potential gradient. A simple geometry for this is the major axis of a ...
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0answers
31 views

Do you know if you have zerovalent iron nanoparticles in liquid how to measure minimal magnetic force required for separation of these nanoparticles?

I think of measuring mag susceptibility from VSM data (magnetization divided by the applied field) but I am not sure if this would be enough. Maybe if I employ SQUID measurements, but in that case I ...
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2answers
606 views

Curl of a simple magnetic field and resulting current distribution

I've been doing some thinking lately and here is my question: If one imagines that there is an auxiliary magnetic field $H$ whose spatial dependence is given by equation: $$H(x,y,z)=y\hat{i}$$ ...
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1answer
1k views

Electric flux density for a hollow cylinder using Gauss's law [closed]

In the textbook of "Engineering Electromagnetics": I understood it except the part highlighted with yellow(i.e. how did he find the charge distribution of the outer cylinder? What are the principles ...
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0answers
31 views

Why do magnetic forces scale down so poorly?

Im told by experts in MEMS and nanotech that magnetic forces scale down very poorly. This is one reason we have many MEMS devices based on electric forces/electrostatics but not on magnetics. Can ...
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0answers
69 views

How to understand Steady Currents within the limits of Magnetostatics

I know that the precise mathematical statement of local charge conservation is $\nabla \cdot \vec{J}=-\frac{\partial \rho}{\partial t}$, where $\vec{J}$ is the volume current density and $\rho$ is the ...
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1answer
3k views

Magnetization of soft iron and steel

I was reading and I saw that the steel becomes permanent magnet whereas iron becomes a temporary magnet after magnetization during magnetic induction. Why does soft iron make temporary magnets and ...
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1answer
203 views

Conditions on expressing magnetic field in terms of curl of current density

Given a current density distribution $\mathbf J(\mathbf x)$ inside a closed bounded region $\Omega$, the magnetic field at any point $\mathbf y$ outside of $\Omega$ can be expressed as $$ \begin{...
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2answers
684 views

Most fundamental quantity in magnetostatics and magnetodynamics [closed]

In both elctrostatics and electrodynamics, the electric charge is defined as the most fundamental quantity. What is the most fundamental quantity in case of magnetostatics and magnetodynamics ?
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2answers
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Does Biot-Savart law apply in changing electric field or it needs a modification just like Ampere's law, to become as true as Maxwell's 4th equation?

Does Biot-Savart law apply in changing electric field or it needs a modification just like Ampere's law, to become as true as Maxwell's 4th equation? In the update to Ampere's circuital law, the ...
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4answers
5k views

What is the difference between the magnetic field of a permanent magnet, and that of an electromagnet?

What is the difference between the magnetic field of a permanent magnet, and that of an electromagnet? In the diagram below, you can see that the magnetic field of a wire which carries a DC ...
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2answers
979 views

How to get image current in magnetostatics? (magnetic slab)

I want to know the image current and its location which satisfies the boundary condition at the interface. This problem was originated from the problem 6-33 in Fields and wave electromagnetics, D. ...
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1answer
276 views

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 ...
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2answers
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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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1answer
717 views

Magnetic field between two rings [closed]

Two rings are placed parallel atop each other along an axis with a distance $\epsilon$ which is much smaller than the radius of both rings a. Through one of the rings there is a current I and through ...
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1answer
1k views

The magnetic field between two intersecting cylinders [closed]

Consider a cable of infinite length whose section has the form of two intersecting circles of same radius $a$. The first part is then a cylinder of constant volume current density $J$ along the ...
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0answers
1k views

Force between two current carrying wires: the general case

Assume two straight current carrying parallel wires with currents ($I$ and $I'$) flowing in the same direction, at a distance $R$ from each other. From Ampère's law (and from Biot-Savart as well) it ...
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1answer
2k views

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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1answer
737 views

Why is the circumferential component of the magnetic field around a solenoid zero?

According to Introduction to Electrodynamics by Griffiths, the reason is "$B_{\phi}$ would be constant around an Amperian loop concentric with the solenoid, and hence $\int{\vec{B} \cdot d\vec{l}}=B_{...
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1answer
558 views

Magnetic Field Along the Axis of the Current Ring - Alternative way to compute

This is Example 5.6 in Griffith's Introduction to Electrodynamics (4th Edition): Find the magnetic field a distance $z$ above the centre of a circular loop of radius $\ R$, which carries a steady ...
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1answer
370 views

How to approximate the force on a magnet below a coil

o x o x Coil with 4 turns o x o x _ | | | | Neodymium magnet |_| I need to know the ...
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0answers
231 views

Where can I find actual data for the hysteresis of a magnetic material?

When a magnet is exposed to an external magnetic field it can be further magnetized or demagnetized. This amount can be found by looking at the hysteresis curve for that magnet. I do not have the ...
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1answer
2k views

Finding the vector potential of an infinite cyclinder with uniform surface current

This is the second part of a problem in Griffith's "Introduction to Electrodynamics 4th Edition" (problem 6.16). The first part was to find the magnetic field inside a coaxial cable (2 concentric ...
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1answer
482 views

How do you show that the normal derivative of the magnetic vector potential is discontinous across a surface current?

This is from Griffith's "Introduction to Electrodynamics" 4th edition, problem 5.33. I need to show that $$ \tag 1 \frac{\partial \textbf{A}_{above}}{\partial n}-\frac{\partial \textbf{A}_{below}}{\...
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198 views

What are some open problems in classical electrodynamics? [duplicate]

I am about to finish reading 'Introduction to Electrodynamics' by David Griffiths. Throughout the textbook, Griffiths makes frequent references to current literature (mostly articles from American ...
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0answers
71 views

Anyone know of a flow chart or list of common/useful consequences of Maxwell's equations?

I just recently started to appreciate the Maxwell equations. I had never really take the time to study them but I feel like I'm finally more familiar with them. I've noticed that it seems like a lot ...
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2answers
236 views

Can a charge moving in an open trajectory qualify as current?

It is sometimes said that a point charge is equivalent to an electric current. If it were a steady current, I should be able to find it from Ampere’s law or Biot-Savart’s law. Even if the current is ...
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0answers
71 views

can magnet used in engines

My friend has told an idea that if the same poled magnets are placed in the motors instead of engines,it will produce the ultimate energy.because same poles are repelling each other. is it possible?
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1answer
287 views

Lifetime of the magnetization of a ferromagnet

In a ferromagnetic material, there's spontaneous magnetisation, meaning in the absence of a $\mathbf{B}$ field $\mathbf{M}\neq 0.$ This means that there may be different domains in the sample where ...
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2answers
1k views

Why is there a magnetic field around a magnet if there are no charges moving? [duplicate]

From what I understand, the magnetic force is just a relativistic effect of the electric force, and I understand how this is can be the case when considering the magnetic field generated by a current- ...
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1answer
142 views

Building huge magnetic field gradient

Looking at how MRI works, I came across the fact that the spatial resolution depends on the magnetic field gradient, this gradient being created by "gradient coils". I was not able to find what the ...
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0answers
906 views

Uniformly magnetized sphere

While working on a uniformly magnetized sphere, I have come across this problem: How does the boundary value equation $$\vec n.(\vec B_2-\vec B_1)=0$$ lead to the equation $$\phi_{out}|_{r=a}=\phi_{in}...
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4answers
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How would you define electrostatics and magnetostatics starting from Maxwell's equations?

I'm reading Griffith's text, and he starts by defining Electrostatics as requiring the source charges don't move. I've seen a few slightly different definitions of electrostatics and magnetostatics. ...