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Questions tagged [magnetostatics]

The study of magnetic fields in systems where the currents are steady (not changing with time). It is the magnetic analogue of electrostatics, where the charges are stationary.

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From what equations is magnetic field uniquely determined for a given current distribution?

The Maxwell equations for magnetostatics in the absence of time varying electric field state that - $$ \mathbf{\overrightarrow{\nabla}} \cdot \mathbf{\overrightarrow{B}} = 0 $$ $$ \mathbf{\...
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Magnetic Dipole Derivation

$\oint (\hat{r}\cdot \vec{r}') d\vec{l} $ is what I get as part of the magnetic dipole term, but I can reduce this to $ -\vec{r}' \times \int d\vec{a}' $. I don't understand how you can reduce it to ...
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Force on an iron core in a solenoid?

Consider the following textbook problem: An iron core ($\mu_r > 1$) of length l is inserted into a solenoid with N turns of the same length, through which runs the DC current I, up to a length $0 \...
BlenderBender's user avatar
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Do moving charges still generate an electrostatic field?

According to my EM professor, an infinite line of current $I$ creates only a magnetostatic field (the regular $\vec B=(\mu_0 I\vec /2\pi r)\vec e_\varphi$ you get from applying Ampère's law), and not ...
Lagrangiano's user avatar
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Where comes the Biot-Savart formula from? [duplicate]

I learned about the Biot-Savart Law recently. I understand how to calculate magnet fields with it, but where does this formula $$dB=...$$ come from? My professor just told me we do that in theoretical ...
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Wrong representation of the field of an axially magnetized ring magnet floating on the internet?

I always thought that the field of a short length axially magnetized ring magnet resembles this illustration here of Fig. 1 similar to the magnetic field of a single current loop: Fig.1 Axial Ring ...
Markoul11's user avatar
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Green's function solution in 2D for the potential of solenoids in the Lorenz gauge

My main goal is to find a general expression for the potential in the Lorenz gauge of some solenoidal (not necessarily circular) current density using the Green's function. I assume that the current ...
Arceon's user avatar
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Doubts regarding the statement "Ampere's circuital law does not depend on Biot-Savart Law"

Here Ampere's circuital law is specifically referring to: $\oint{\vec{B} \cdot \vec{dl}}=u_o\cdot I $ , I do not think it's also considering the displacement current, according to the statement. Since ...
makhi1249's user avatar
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Magnetic field outside a sphere containing surface charge rotating at a uniform angular velocity

Say I consider an amperian loop surrounding the sphere, wouldn't the net current through it be zero as the current entering the loop due to one half of the sphere and the current exiting in the ...
Anonymousstriker38596's user avatar
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How does an external magnetic field affect the magnetization inside a permanent magnet?

I am looking for a first-order correction on the intensity of the field generated by a (neodymium) magnet in the presence of an external magnetic field $B$ (possibly generated by another magnet). For ...
Georges's user avatar
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Induced current in a superconductor

I was recently solving a problem from Jaan Kalda's handouts; Parallel to and at a distance $h$ above the surface of an infinite planar superconductor is an infinitely long straight wire with current $...
Cognoscenti's user avatar
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Induction in a magnetostatic scenario

A charge is moving at constant velocity along the x-axis. Question: is there induction occurring, OR, only magnetostatic fields updating as the charge moves at a constant velocity? Let's say the ...
Daniel's user avatar
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Magnetostatics problem involving dipoles

A while back I came across a problem in which I were to find the force of attraction between a magnetic dipole and a spherical iron ball (which is much smaller than the distance between the dipole and ...
I_am_ant's user avatar
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Confusion between two forms of magnetic energy

When an ideal dipole with constant current $\vec{m}$ is in a magnetic field, its "potential" energy is $-\vec{m}\cdot\vec{B}$, which may be used to derive the magnetic force acting on the ...
Jaime Yepes de Paz's user avatar
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Can an electric field shift the magnetic saturation point?

If we expose a magnetisable body to a strong external magnetic field, the generated magnetic field of this body is subject to saturation. If this body is now also subjected to a static electrical ...
HolgerFiedler's user avatar
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Ampere's law for a curved wire

Deriving Ampere's law in magnetostatics for an infinitely long straight wire is pretty straightforward. However is it possible to derive it for any curved wire or that can only be shown to work ...
Krum Kutsarov's user avatar
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Average magnetic field inside a sphere of vacuum in magnetostatic case

For this problem, consider the electric and magnetic fields constant. In this scenario, the average electromagnetic field inside a sphere of vacuum is equal to the electric field at its center. $$ \...
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What is the meaning of $\vec H$ with respect to the total field?

Now before saying anything, I have seen the similar questions in this page regarding $\vec H$ but no one has fully convinced me yet, since I will try to give another perspective to this question. We ...
Ulshy's user avatar
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Is magnetostatics a more idealized regime than electrostatics?

The electrostatic regime only needs to consider that $\rho\neq \rho(t)$ and $\mathbf{J=0}$ and from there all the common results follow. Notice that $\mathbf{J=0}$ comes naturally if you assume that ...
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Replacing magnetic field with electric by replacing currents with charges

In a region where there are no currents, the magnetic field follows the same equations as the electric field in a region with no charge density. $$\nabla \cdot \vec B = 0 = \nabla \cdot \vec E$$ $$\...
SuspiciousGarbage's user avatar
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Why does the direction of the magnetic potential vector follow the current?

In Griffith's textbook, it is said that the vector potential $\vec{A}$ usually points in the direction of $\vec{J}$: This was also pointed out in class. However, I don't understand why it should be ...
Jaime Yepes de Paz's user avatar
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Expression vectorial to magnetic field $\vec{H}$ in conductor region

I have some difficult to figure out the second expression about the contribution of magnetic field as you see below: Problem: A wire conductor, infinite long (Z axis), conduct a current constant equal ...
miguel747's user avatar
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Magnetic vector potential of a current loop results in 0 in all space

I tried applying the following relation $$ \vec{A} = \frac{\mu_0}{4 \pi} \int_\Omega \frac{\vec{J}}{\vert \vec{r} - \vec{r}^\prime \vert} dV$$ To find the magnetic vector potential on all space of a ...
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Problem with derivation of $U_B=-\mu \cdot \vec{B}$

I'm trying to prove that $U_B=-\mu \cdot \vec{B}$, but I keep running into an annoying dead end in my proof (a note about the notation my course's instructor uses: $\mu$ = magnetic moment, $NIA \hat{n}...
JBatswani's user avatar
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How to interpret Magnetic Susceptibility as the ratio of two vectors $M$ and $H$, as division of two vectors is not defined in mathematics?

Magnetic Susceptibility, denoted as χ is defined as a scalar, represents the ratio between the Magnetization vector ($\vec {M}$) and the Magnetic field strength vector ($\vec{H}$). However, in ...
Dinesh Katoch's user avatar
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If the conductor floats in a horizontal homogeneous magnetic field, what is the current?

If the conductor floats in a horizontal homogeneous magnetic field, its magnetic flux density is 0.75 T and one meter of conductor weighs 2.5 g. How to calculate current. So when the length or mass is ...
Violettttt's user avatar
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3 answers
81 views

Which electromagnetic coil would have a stronger magnetic field, High amperage low voltage or low amperage high voltage?

My apologies if the question is just too simplistic, I asked to ChatGPT and it said that the high amp low volt coil would be the strongest, I just want to confirm. Assuming that both have the same ...
Fulano's user avatar
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2 answers
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Still can't see why $\nabla \times \mathbf J(\mathbf r') = 0$ in Biot-Savart derivation

When deriving the differential form of Biot-Savart's law (which is also Ampere's law under magnetostatic conditions) there is one step which I am still not fully convinced. We will firstly use this ...
rr1303's user avatar
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Computation of surface bound current: ambiguity in the choice of a normal unit vector for a surface

Let us suppose to have two coaxial cylindrical tubes, namely two cylindrical surfaces $\Sigma_1, \Sigma_2$, with a radius of $a$ and $b$ respectively. A current $I$ flows across the surfaces but in ...
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Force on infinitesimal loop as stated in Griffiths' Electrodynamics

I've found little to no success in finding a proof of result given by Griffiths at the start of the chapter on Magnetic fields in matter, namely the one for the force acting on an infinitesimal loop ...
Claudio's user avatar
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Force on a circular loop formulae in Griffiths' Electrodynamics

I'd like to ask for some clarifications on the formulas for the force on a loop with magnetic dipole moment immersed in a non-uniform magnetic field, given by Griffiths in Introduction to ...
Claudio's user avatar
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Torque on a current loop in a uniform magnetic field

I'm trying to prove the result the net torque on a current loop in a uniform magnetic field is $\vec{\tau}_{net}=\vec{\mu}\times \vec{B}$ where $\vec{\mu}=I\frac{1}{2}\oint(\vec{r}\times d\vec{r})$ ...
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Derivation of discontinuity of vector potential

I'm trying to prove the equation from Griffiths' Introduction to Electrodynamics which tells us that the vector potential ${\bf A}$ is continuous across any boundary (both tangential and normal ...
Claudio's user avatar
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Magnetostatics: Boundary conditions

I'm reading chapter 5.4.2 of Griffiths' Introduction to Electrodynamics, and I'm having trouble understanding some of the reasoning and some of the results he obtains. He starts by considering a ...
Claudio's user avatar
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Point dipole approximation limit

Can I approximate the field of a 10 mm length x 5 mm radius cylindrical magnet at 8 mm away using a point dipole approximation? I was wondering if it would still be possible to create a semi-accurate ...
ggggggggg's user avatar
2 votes
2 answers
660 views

Metals and Magnets

A metal is attracted by a magnet when placed in it's vicinity. I was wondering if it is the metal that moves towards the magnet, or is it that both the metal and magnet move towards each other? Could ...
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2 answers
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Magnetic field outside of permanent magnet - What is $\vec H$?

If a cylindrical magnet has a uniform magnetization $\vec{M}$ along its axis its magnetic field $\vec{B}$ looks approximately like this: There seems to be a contradiction to me. Since there are no ...
J. Grohmann's user avatar
1 vote
1 answer
61 views

Biot-Savart integral over a half-ellipse does not seem to approach the result on the line

I am trying to compute a Biot-Savart integral of the vector potential over one-half of an elliptic path, however as a check I compared the result when the ellipse becomes "squashed" as an ...
UnkemptPanda's user avatar
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Does this basic example of two bar magnets preserve angular momentum conservation?

Let's say I hold two bar magnets side by side both vertically aligned ($z$-axis). I don't want to worry about their shapes, so let's approximate them as dipoles. I will use the dipole formula rather ...
Maximal Ideal's user avatar
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1 answer
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Biot-Savart for two infinite wires with U turn

Consider this arrangement ...
TeamPhysics's user avatar
1 vote
2 answers
86 views

Ampere's law on infinite path

I was calculating the magnetic field of a circular current loop using Biot-Savart law and obtained it straightforwardly. If the loop is in the $xy-$plane, centered at the origin, the field at a point ...
EM_1's user avatar
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Confusion on Griffith's Electrodynamics Example 5.3

In the fourth edition of Introduction to Electrodynamics, a scenario is described in example 5.3 where a rectangular loop of wire supporting a mass $m$ hangs vertically with one end in a uniform ...
Scott's user avatar
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Enforcing Mathematical Continuity for a System Containing Discontinuity

I am attempting to numerically solve a BVP for a solid core solenoid field. I am starting with: $\vec{\nabla{}^2}\vec{A_r}=0$ $\vec{\nabla{}^2}\vec{A_\phi}=\frac{\mu}{\mu_0}\vec{J_\phi}$ $\vec{\nabla{}...
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Magnetization Enhancement Using Various Materials

I was looking online at how inserting a material inside a solenoid can enhance/reduce the magnitude of a magnetic field in all space depending on what material is inserted. This makes sense from a ...
Sophia's user avatar
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1 vote
1 answer
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Computing mutual inductance given only magnetic fields

I am experimenting with numerically computing the mutual inductance between a number of coils in the presence of various magnetic materials. Traditionally, the mutual inductance is found by ...
unknownperson's user avatar
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336 views

Magnetic flux in a loop from a circular coil

Problem At the center of a circular coil with length $L$, radius $b$ and $N$ windings is there a small circular ring with radius $a << b$. The ring is coaxial with the axis of the circular coil....
Tanamas's user avatar
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1 answer
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Not understanding Ampere's law

Suppose we have some wire of length $2b$ with a current $I$ flowing through it and we want to evaluate the field at some distance $a$ radially outwards from the centre of the wire (so a distance b ...
David's user avatar
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1 answer
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Conservation of Momentum violation with Lorentz Force

Note: I am describing this question using cylindrical coordinates $\hat{r}$, $\hat{\theta}$, $\hat{z}$. I've been looking into how you could slow down a plasma moving downstream in a pipe using ...
Gage Gardinier's user avatar
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Pressing force of a solenoid

If a current is passed through bundle of loosely coiled, insulated wire the space between the wires rapidly contracts, crushing it down into a disk. How can this crushing force be calculated? I know ...
WaveInPlace's user avatar
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2 answers
152 views

Can we use Ampere's law without requiring help from Biot-Savart law?

Consider the case of a straight, infinite wire carrying uniform current. From reversing the direction of the current we can rule out radial dependence of the magnetic field but are left with two ...
GedankenExperimentalist's user avatar

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