Questions tagged [magnetostatics]

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23 views

Why does a polarized material generate a depolarizing field?

I do not understand how a polarized material (steady state, no free current, no free charge) can generate a depolarizing field. Based on https://en.wikipedia.org/wiki/Demagnetizing_field, I "...
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1answer
19 views

Magnetic field inside a ferromagnetic material

Let us suppose there is a block of a ferromagnetic material inside a very long ideal solenoid. We know that the magnetic field lines inside are always in a straight line which will be perpendicular to ...
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1answer
36 views

Electrostatics and Magnetostatics as Field Theories ( isn't the Coloumb law depicting an instantaneous action at a distance)

Take the formula for Coloumb's law. It does not show in any case as to how the static field propagates. What I can feel is that the field of a static charge is ever prevading from the time the charge ...
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2answers
57 views

Neat expression for the dipole potential in Fourier space?

In textbook electromagnetism we are used to seeing neat, coordinate-free, expressions for the scalar potential from an electric dipole (using Gaussian units) $$\phi(\mathbf{r}) = \frac{\mathbf{p} \...
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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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0answers
56 views

Magnetic field of rotating disk with non uniform volume charge $\rho_{f}=k(R-s)(d-z)^{2}$ [closed]

Consider a thin disk ($d \ll R$, with thickness $d$ and radius $R$), with volume charge distributed as $\rho_{f}=k(R-s)(d-z)^{2}$, where $s=\sqrt{x^{2}+y^{2}}$ and the coordinate origin $(x, y, z)=(0,...
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3answers
108 views

Can a static non-conservative vector field have scalar potential?

STATEMENT#1: A vector field can be considered as conservative if the field can have its scalar potential. STATEMENT#2 If we can have non-zero line integral of any vector field along with a single loop ...
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1answer
150 views

Method of images in cylindrical coordinates for a circular ring of current

I am trying to determine if the following problem has an analytical solution using the method of images. The problem is an infinitely long (in $z$) cylinder of a material with permeability $\mu_2$ of ...
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1answer
2k views

Why use the method of images in magnetostatics?

If a current is above a conducting surface, why do we take the image of the current to find the magnetic field intensity? Why not just take the effect of the actual current only? And are this method ...
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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 ...
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0answers
44 views

A theory where it's convenient to express a scalar quantity as a divergence of a vector

The equations of electrostatics,$$\nabla \cdot \vec{E} = \rho, \quad \nabla \times \vec{E} = 0$$make it possible to introduce the scalar potential $\vec{E} = - \nabla \phi$, which then satisfies the ...
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2answers
31 views

Under what conditions can we use Ampere’s law to find magnetic fields?

I'm trying to understand the different formulas to calculate magnetic fields, it looks like Ampere’s law is an easier way than the Biot-Savart Law, but only works under certain conditions (similar to ...
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0answers
36 views

Trying to derive the force on the local current distribution in the external magnetic field

I am trying to derive the formula of the force on local current distribution in an external magnetic field as shown below. Since $ \ \ \ {d \hat F=I \ d \hat L \times \hat B} \ \ $, I come up with the ...
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1answer
41 views

Force of moving magnetic field on stationary charge

I heard that a magnetic field only creates a force on a moving charge, not a stationary one. However, what if the solenoid containing the magnetic field was moving through a stationary charge. Would ...
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1answer
25 views

Current - magnetic field intensity relation [duplicate]

This is my first question in this community and I hope to get a good answer. I'm reading a book about the principles of electrical machines and it is in English while my first language is Arabic, so I ...
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0answers
24 views

Hysteresis loop in Griffiths' Introduction to electrodynamics

In Griffiths' Introduction to electrodynamics there's the following Hysteresis Graph: Shouldn't it be $10^{-4}$ instead of $10^{4}$ on the x-axis?
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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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1answer
28 views

Does electromagnet work without heat of wire?

If we isolate wire with thin wire and assuming that no heat rejected by wire then does electromagnet work. If it work then it violate conservation of energy .
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3answers
583 views

Magnetic scalar potential far above a magnetic film

The situation I am looking at is a magneto-static problem of a finite magnetic film with magnetization $\bf{M}$. I would like to find the the magnetic field far above the plate. My expectation is that ...
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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

Why would a ring magnet's flux decrease once distance starts getting small?

I went ahead and use python magpylib to simulate a ring magnet joystick, and then graph flux over distance of the ring magnet. Here's the code: ...
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1answer
31 views

What is a magnetization vector, and how can it be computed?

So I know that this is a physics related site, but I'm trying to use a Python library called magpylib to compute magnetic flux at various positions from a joystick ...
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1answer
29 views

The amount of current needed to accelerate for specific speed

In the magnetic gun a conducting rod is placed on a two rails connected to a voltage source, so that a current can flow in the rod. Magnetic field $\vec{B}$ is applied perpendicular to the rail-rod ...
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1answer
36 views

Magnetic field on an arbitrary point ON a Current Loop

Consider this situation given above. We have an arbitrarily shaped theoretical current loop made up of wire of zero radius in free space. Away from all electromagnetic, gravitational interactions. ...
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1answer
39 views

Formula of magnetic flux through a loop as a function of time

I was studying Lenz's law and self inductance when I came across the following question. Take R to be the radius of a circular loop, which has a magnetic field perpendicular to this loop. We let 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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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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0answers
13 views

How to prove that magnetic flux density satisfies Ampere's Circuital Law

Here is the expression for Magnetic flux density B which derives from Magnetic vector potential A. I have trouble proving that B in this equation satisfies the differential form of Ampere's Circuital ...
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1answer
52 views

Magnet modeling

I wrote simple physics mass-spring engine, and I want to add the magnetism. Each body consists of tiny connected spheres with some mass. The only input values to calculate magnetic interactions I ...
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0answers
61 views

How do you prove $\int (x^ij^k+ x^kj^i)\,\mathrm d V =0$?

I have got a problem when trying to calculate the second term of the expansion of the vector potential $\boldsymbol A$. My textbook gives me a formula yet without proof. The problem is to prove $$ \...
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1answer
42 views

Current Density as a 3D Function

I have a three dimensional current carrying coil. This coil has rectangular cross section, with a rectangular hole cut in the middle. The aim is then to assign the current density at points inside the ...
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4answers
4k views

Why is the magnetic field due to an infinite current sheet constant throughout all of space?

By Ampere's Law, using a rectangle as an Amperian loop, I know that it can be derived that the magnetic field is constant throughout all of space (i.e. it does not depend on the distance r from the ...
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3answers
709 views

Violation of Amperes circuital law

How does the magnetic field expressed in perfectly straight lines from a magnetic north pole to a south pole violate amperes law?(As my textbook says that it will ) On the contrary, what would make ...
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2answers
375 views

Find torque due to Lorentz force - Wrong result

Current I is coming from the Z axis and then it flows out uniformly towards the circumference of this disk. The disk has thickness t and Radius R. There is also a constant B field in the Z direction(...
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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
3k views

What is the permeability of a permanent magnet?

The following is a diagram that shows the B- and H-fields of a permanent magnet. Inside the magnet, the H-field is in the opposite direction to the B-field, because of the magnetisation M-field and ...
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1answer
64 views

Current density $\mathbf{J}$ of particle with magnetic dipole moment $\mathbf{m}$ [closed]

I'm solving some excercises on magnetostatics, and encounterded this on which i'm having some trouble. Given a particle of magnetic dipole moment $\mathbf{m}$, show that its current density is given ...
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0answers
51 views

Why does magnet attract and push each other? [closed]

Why do magnet attract and push each other? This question seems easy, but in fact, it is big, maybe as big as trying explaining gravity with quantum physics to the origin that how each particle ...
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1answer
67 views

Boundary Conditions in Magnetostatics - Calculating surface current density

I'm working on a finite element simulation of the magnetostatic magnetic vector potential in 3D, with the following geometry:. The internal structure is a hollow cored-rectangular current loop. The ...
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0answers
50 views

Compute permanent magnet movement in magnetic field

Assume I have tiny magnet particles in vacuum, which are not considered as a points, although they are very tiny. Magnet particles are situated in a uniform magnetic field. How can I can describe the ...
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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
69 views

Magnetic field through ferromagnetic cylinder when length is much bigger than the radius?

To preface, this is indeed a homework problem. I am a mathematician taking an electromagnetism module and have trouble wrapping my head around the problem at hand, and am struggling to start a ...
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0answers
22 views

magnetostatics and electrostatics orbiting an object with a field

I understand from the Feynman notes on physics how a static magnetic field in one frame of reference becomes a static electric field in a reference frame in which I move at the same speed as the drift ...
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1answer
46 views

Coulomb gauge in magnetostatics should give divergence-free vector potential

Say we're dealing with magnetostatics ($\vec{\nabla} \cdot \vec{j} = 0 $). If we define $\vec{A}$ to satisfy $\vec{B} = \vec{\nabla} \times \vec{A}$, and we take the assumption that $\vec{\nabla} \...
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1answer
829 views

Moving charges and steady current

Steady currents generates a constant magnetic field-magnetostatic Formally, this is $\frac{\partial \vec{J}}{\partial t}=\vec{0}$ Any currents steady or otherwise are due to the movement of point ...
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0answers
129 views

Total current for an arbitrary current density

Imagine a localized region $\mathcal{R}$ which contains a current density $\mathbf{j}$, which we take to be divergence-less, $\mathbf{\nabla\cdot j} = 0$. What is the total current associated with ...
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30 views

How do I prove that the integral of a dot product of position vector and current distribution over all space is zero?

I am currently taking intro electrodynamics. My professor showed us that the for a current distribution $\vec{j}(\vec{r})$, the following relation is true: $\int d^{3}r' j_{k}(\vec{r}') = 0$ And I ...
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107 views

Permittivity and electric Susceptibility intuition

I have a question on the intuition behing the relation between relative permittivity $\epsilon(\omega)$ and electric susceptibility, $\chi_e$ of a of a material, more precise a dielectric medium. ...
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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{\...
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28 views

Guoy method derivation, or, how not to break math?

I start from $d\vec{F}=\nabla(\vec{m}\vec{B})$, $\vec{M}=\frac{d\vec{m_i}}{dV}$, and $\vec{M}=\frac{\chi_v}{\mu_o}\vec{B}$. I write out the definition of the force, determine we're only interested ...

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