Questions tagged [magnetostatics]

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How to derive Biot-Savart's law for the magnetic field of a surface charge

The Biot-Savart law gives the magnetic field of a steady line current: $$ B(r)=\frac{\mu_0}{4\pi}\int\frac{I\times\hat r}{r^2}dl. $$ Now according to Griffiths, for surface currents, the Biot-Savart ...
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2answers
60 views

How do magnetic shields work?

I've come across the fact that magnetizable material can shield magnetic fields. For example, if I put a ferromagnetic plate between the magnet and a nail that is hanging on a thread pulled towards ...
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2answers
78 views

Cancellation of surface integrals (involving Maxwell's equation)

In our physics class today, we wanted to derive ${curl}(\bar B) =\mu_0 \bar j $ from the Maxwell equation $$\oint_C \bar B(\bar r).d\bar l = I_{net}\mu_0$$ We did this using Stokes theorem, and in ...
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1answer
306 views

What is the physical quantity which makes a Reed switch open or close?

I would like to generate the activation map of a Reed switch, similar to the following: Using a magnetic finite element modeling software such as FEMM. Assuming the Reed switch closes for X Ampere-...
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0answers
88 views

Force Lines of Magnetic Field of Circle Loop

Magnetic field of a loop with a stationary current in a xy plane with center in the origin is usually computed on the z axis. Out of the z axis the calculation results into elliptic integrals. I would ...
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2answers
989 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
4k views

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
2k views

Behaviour of a magnetic compass needle near a magnet

We all know that a magnetic compass needle when suspended by a thread and placed near a bar magnet, will rotate. However like a bar magnet, will the magnetic compass needle get attracted towards the ...
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1answer
1k views

Finding the vector potential of a spinning spherical shell with uniform surface charge?

I have problem solving the following magneto-static problem. I would greatly appreciate help and guidance. This is how the problem is stated: A spherical shell of radius $R$, carrying a uniform ...
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0answers
204 views

Is current always constant with time in electrostatics?

In electrostatics, electric and magnetic fields are not time-variant. In that situation, I guess that current must be stationary. Otherwise, $\partial E/\partial t \ne 0$ because if it were stationary ...
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1answer
84 views

Work by magnetic field [duplicate]

we all know that magnetic field doesn't work....if a current carrying element pulls a metal piece then work is done by the source or the battery not the field.....now let us assume that a bar magnet ...
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1answer
2k views

Magnetic Scalar and Vector Potential

Electric potential is single value since curl E =0. According to me magnetic scalar potential should be single valued ( since curl B=0) and the vector potential should be multi valued. I can just not ...
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1answer
442 views

Vector Potential and Zero Divergence

In the following problem and many others in magnetostatics (Griffiths book) I'm asked to check that $\nabla . A = 0$. While "It is always possible to make the vector potential divergenceless." also "...
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1answer
103 views

How does the continuity of $\bf A$ ascertain the parallel components $\boldsymbol\nabla(A_{i,1}-A_{i,2})$ being zero but not the normal one?

I was reading in this pdf about the discontinuity of the derivative of the vector potential $\mathbf A$ across a boundary with $\hat{\mathbf n}$ acting as the normal to the plane having surface ...
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4answers
6k views

Why is this vector field curl-free?

The curl in cylindrical coordinates is defined: $$\nabla \times \vec{A}=\left({\frac {1}{\rho }}{\frac {\partial A_{z}}{\partial \varphi }}-{\frac {\partial A_{\varphi }}{\partial z}}\right){\hat {\...
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1answer
104 views

Ill-defined $\mathbf{H}$ field for uniformly magnetized space?

How does one define the magnetic $\mathbf{H}$-field for a space entirely filled with a uniform magnetization $\mathbf{M}$? I know this sounds silly/trivial, but hear me out. In all of the following ...
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2answers
233 views

magnetic field doing work on a wire

I am a tutor and during a session today, a thought occurred to me. I've long been told (and been telling) that magnetic fields do no work, but it's pretty easy to imagine a situation in which a ...
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2answers
1k views

Ampère's law applied on a “short” current-carrying wire

Why doesn't Ampère's law hold for short current carrying wires? Of course, such wires should be part of a closed circuit, but that's a physical fact, and there is a numerous amount of ways to close it....
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1answer
588 views

Induced current in a circular loop [closed]

In this question I tried using right hand thumb rule for long wire to get magnetic field into plane of paper which induces clockwise current in Loop,again by thumb rule. The problem arises when force ...
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1answer
453 views

For a constant magnetic field, is there a gauge with both canonical momenta conserved?

To describe a constant magnetic field $\mathbf B=(0,0,B)$ (ignoring the motion along the $z$ dimension) within hamiltonian (or quantum) mechanics, one needs to choose a gauge. One common gauge is the ...
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4answers
2k views

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. ...
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1answer
436 views

What are the advantages of Magnetocardiography?

I am reading the book Bioelectromagnetism by Malmivuo: Difference between the bioelectric and biomagnetic measurements lies in the sensitivity distributions of these methods. Diverse technical ...
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1answer
1k views

Force on circular current loop in non-uniform magnetic field [closed]

First off I'm not very good with the physics so if this is easy please excuse my ignorance. The question is asking me to find force on a circular current loop with current I. It is placed in a ...
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0answers
62 views

Would setting a magnetic base to the “off” position remove the torque from an external field?

A magnetic base is a permanent magnet mostly inside a ferromagnetic case. It can be rotated so that the field is either internally shunted through the ferromagnetic blocks, or so that the blocks are ...
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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
459 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
657 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
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 ...
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81 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 ...
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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
302 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
258 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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2answers
801 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
478 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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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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0answers
272 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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2answers
621 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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1answer
7k views

Magnetic field of uniformly charged rotating hollow sphere

I want to compute the magnetic field due to a homogeneously charged, rotating sphere with radius $R$, angular velocity $\vec{\omega} = \omega\hat{z}$ and total charge $Q$. I want to use Biot-Savart ...
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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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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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71 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
719 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
30k views

Magnetic field inside and outside cylinder with varying current density [closed]

I am reading through Introduction to Electrodynamics by David J. Griffiths and came across the following problem: A steady current $I$ flows down a long cylindrical wire of radius $a$. Find the ...
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2answers
692 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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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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1answer
277 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
3k views

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 ...