Questions tagged [magnetostatics]

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37 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
26 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
32 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
34 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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11 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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60 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
50 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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1answer
38 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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1answer
62 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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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
52 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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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 ...
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66 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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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
44 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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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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99 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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0answers
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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40 views

Why is $A \propto 1/r^3, B \propto 1/r^4$, far away from circular loops

Two equal circular current loops are placed coaxially with each other. The loops have equal but opposite currents $I$. $$ A \propto r^{-l} $$ $$ B \propto r^{-k} $$ , where $A$ is the vector ...
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1answer
213 views

Cylindrical shell in magnetic field [closed]

Exercise: 'Infinitely long cylindrical shell of inner radius a and outer radius b of material of magnetic susceptibility χ is placed in otherwise uniform magnetic $B_0$ perpendicular to cylinder's ...
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52 views

Deriving the formula for the magnetic field of a Helmholtz coil by using cylindrical coordinates

I have following problem: I want to calculate the magnetic field inside a Helmholtz coil but instead of using Cartesian coordinates I want use Cylindrical coordinates. My approach: The Biot-Savart ...
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1answer
127 views

B field and H field inside a bar magnet

Recently I've been studying about magnetism there is one piece of information I'm stuck at . It says that the direction of magnetization and H field inside a bar magnet are opposite. First of all ...
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1answer
130 views

Current Density In a 3D Loop - Discretising a Model

I'm working on a finite element model as part of a line of research. Specifically I'm consider using vector finite elements (i.e 3 values x,y,z per node) to solve the Poisson equation in magneto-...
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1answer
77 views

Confusion in boundary conditions of magnetic field

So the matter is I'm really confused about boundary conditions of magnetic fields. Prior to the boundary conditions, I thought that say you have an external magnetic field, $B_0$, now if I place a ...
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3answers
71 views

What determines whether we use a vector or scalar potential?

I understand that electrostatic potential is scalar because the curl of the field is zero, and this implies the electrostatic field is the gradient of the scalar potential to satisfy this. Similarly ...
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2answers
106 views

Why is a steady current uniformly distributed across the cross section of a wire?

I came across this question. The question asks for a solution to this problem: Using relevant equations for E and J, show that the current in a steady current I in a cylindrical conductor with ...
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3answers
91 views

Conceptual Understanding of Zero Curl in Ampere's Law

I understand that Ampere's law tells us that the current density times $\mu_0$ at some location must be equal to the curl of $\mathbf{B}$ at that location. However, conceptually this is troubling me. ...
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1answer
336 views

“Derivation” of continuity equation

The surface integral of j over a surface S, followed by an integral over the time duration t1 to t2, gives the total amount of charge flowing through the surface in that time (t2 − t1): $${\...
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1answer
142 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 ...
2
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2answers
290 views

Derivation of Ampere's Law from Biot-Savart

Our aim is to derive $\nabla\times \mathbf B=\mu_0(\mathbf J+\epsilon_0\frac{\partial E}{\partial t})$. To begin with, let $ \mathbf A=\frac{\mu_0}{4\pi}\int_{\mathbb R^3}\frac{\mathbf J(\mathbf r')}{...
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57 views

Solving the Line Integral in Ampère's Law mathematical correctly

Imagen we have a infinite long, cylindrical conductor with radius $\varrho_0$ and $\textbf{j}=\begin{cases}j_0 \textbf{e_z} &r\leq \varrho_0\\ 0 &r>\varrho_0\end{cases}$ We have Ampère's ...
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1answer
84 views

An absurd consequence of magnetic field as an axial vector

One of the definitions of magnetic field (in free space): Force on magnetic north pole per unit pole. Magnetic field is an axial vector. So it changes its sign when we use left handed coordinate ...
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1answer
28 views

Motion of particle in uniform magnetic field with friction propositional to velocity [closed]

A positively charged particlewith charge "q" is at $ (0,0,0)$.There is a uniform magnetic field $ \vec B= -B \hat k$. The particle is given velocity $\vec u= u \hat i$. A resistive friction acts on ...
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1answer
874 views

Magnetic field of an infinite hollow cylinder (with volume current)

Consider an infinite hollow cylinder with inner radius $a$ and outer radius $b$. The volume current density flows anti-clockwise across the surface of the cylinder ($\vec{J} = J\hat{\phi}$). The ...
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3answers
41 views

Magnetic force on current carrying wire

when we keep two wires near each other then they will experience same force is it then correct to explain by newton's 3rd law? -
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215 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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230 views

Are there cases where $\nabla\cdot\iiint\frac{\mathbf{J}(\mathbf{x}')}{\left|\mathbf{x}-\mathbf{x'}\right|}\mathrm{d}V' \neq 0$?

In Jackson's Classical Electrodynamics, Section 5.4 (Vector Potential), the author seems to assume that because $\nabla\cdot\mathbf{J} = 0$, the following holds for the current density (where the ...
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1answer
53 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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2answers
50 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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2answers
110 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
47 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
43 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
121 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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40 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
42 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
66 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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20 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
63 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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