Questions tagged [magnetostatics]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0
votes
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} \...
0
votes
1answer
839 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 ...
6
votes
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 ...
0
votes
0answers
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 ...
0
votes
0answers
120 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. ...
2
votes
6answers
862 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{\...
1
vote
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 ...
0
votes
1answer
42 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 ...
-1
votes
1answer
300 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 ...
6
votes
6answers
8k views

Why is curl of current density $\nabla \times \vec{J}$ equal zero?

I am revisiting the derivation for $\nabla \cdot \vec{B} = 0$ in magnetostatics for the field $\vec{B}(\vec{r})$ of a charge $q$ at position $\vec{0}$ with velocity $\vec{v}$. It proceeds like \begin{...
1
vote
1answer
142 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-...
1
vote
1answer
84 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 ...
0
votes
0answers
53 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 ...
0
votes
1answer
153 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 ...
2
votes
3answers
88 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 ...
1
vote
2answers
115 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 ...
-1
votes
3answers
93 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. ...
1
vote
1answer
380 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): $${\...
2
votes
2answers
229 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 three to the points ...
5
votes
1answer
1k views

Current geometry and Ampere's law

Under the right circumstances, Ampere's law $\oint \vec H\cdot d\vec \ell=I_{encl}$ can be used to deduce the field $\vec H$ at a point from the current enclosed by the circuit which produces $\vec H$....
2
votes
2answers
330 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')}{...
1
vote
2answers
239 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 ...
1
vote
0answers
58 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 ...
2
votes
1answer
91 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 ...
0
votes
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 ...
0
votes
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? -
1
vote
1answer
1k 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 ...
8
votes
3answers
233 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 ...
1
vote
1answer
56 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 (...
1
vote
2answers
51 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 ...
0
votes
2answers
121 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 \...
1
vote
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 ...
0
votes
1answer
51 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 ...
1
vote
0answers
611 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 ...
0
votes
0answers
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}...
3
votes
1answer
83 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 ...
0
votes
1answer
43 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 ...
0
votes
0answers
21 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 ...
1
vote
2answers
64 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 ...
7
votes
1answer
182 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} + ...
2
votes
1answer
65 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}...
2
votes
1answer
203 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 ...
5
votes
1answer
136 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=\...
1
vote
1answer
92 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 ...
6
votes
2answers
543 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 ...
1
vote
1answer
1k views

Volume integral of current density

I'm currently studying magnetostatics and have a simple question : What is the volume integral of the current density over the whole space in magnetostatics $$\int_{V} \textbf{j} \space d^3\textbf{r}$...
0
votes
1answer
107 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
votes
1answer
130 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\...
5
votes
1answer
189 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 "...
1
vote
1answer
52 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 ...