Questions tagged [magnetostatics]

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765 views

Lorentz force law and Ampère's force law

The Lorentz force law specifies the force of a magnetic field on a moving charged particle, and the Ampere force law specifies the force of a magnetic field on a current carrying wire. I am trying to ...
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1answer
103 views

Are there any south and north poles developed when we flow electric current through a Toroidal Solenoid?

I've read that when current flows in a solenoid it behaves like a bar magnet having both north and south poles. I was wondering how can we visualise north and south poles in a **Toroidal Solenoid".
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1answer
68 views

Why am I getting two different results in emu and SI unit?

I am computing force between two magnetic poles each of one unit pole (in emu) and situated one centimeter apart. In electromagnetic units: $$F_{dyne}=\dfrac{p^2}{r_{cm}^2}=\dfrac{1^2}{1^2}=1 dyne$$ ...
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1answer
63 views

Direction of magnetic field clarification

For a circular wire carrying current $I$ in the counterclockwise direction (in the xy-plane), the magnetic field points in the positive $z$ direction. I tried to understand this more by drawing out ...
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1answer
117 views

Magnetic potential and magnetic field assumptions

I've seen many proofs where you want to find the magnetic field inside and outside a solenoid for example. The author said using symmetry magnetic potential is a function of some variables and discard ...
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2answers
2k views

Magnetic flux through current loop

I am trying to calculate the total magnetic flux through the surface of a current loop. I feel that this flux should be finite and nonzero -- so far any attempt in calculating failed. Can this really ...
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1answer
864 views

What is the correct expression for the magnetic energy density inside matter?

I'll use a magnetized sphere as an example, of radius $R$, with a magnetization density $\vec{M}$. The magnetic moment of the sphere is $\vec{\mu} = \vec{M} \, V$. The magnetic field inside and ...
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1answer
226 views

How to evaluate the Lorentz force at a surface where the field is discontinuous?

I'll take a simple case as an example. You have a constant and uniform magnetic field inside an ideal infinitely long solenoid, with currents circulating all around the thickless coils (so there's a ...
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2answers
359 views

Dipolar magnetic field pressure

It is relatively easy to derive the potential energy stored into the magnetic field of an uniformly magnetized sphere of radius $R$ and total magnetic moment $\mu$ : \begin{equation}\tag{1} U_{\text{...
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1answer
55 views

In which orientations do two planar magnetic shells have maximum attraction/repulsion and no force?

A very thin magnet (one side +ve and other side -ve) is called a magnetic shell. Now for two planar magnetic shells placed near to each other with unlike poles facing each other, there will be ...
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2answers
43 views

Current everywhere in conductor

Amperes Law: $\oint\vec{H}.d\vec{l} = I_{enc}$ Is the current, $I_{enc}$, equal to 0 outside of the conductor ($\rho > a$) because the current density, $\vec{J}$, outside is 0?
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38 views

Two ways, different result: Find torque due to magnetic force on a conductor

We have an AB conductor of length $2L$ and an infinite one coming out of the screen as shown in the picture (a is the distance between the 2nd conductor and the middle of the finite conductor) ...
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2answers
2k views

Biot-Savart law and magnetic field of a ring

I have to calculate the magnetic field along the axis of a ring of radius $R$ on which circulates a current $I$ using the Biot-Savart law. The Biot-Savart law as given in my (really bad) course states ...
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1answer
415 views

Magnetic field caused by 2 rings

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 R. Through one of the rings there is a current I and through ...
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2answers
852 views

Cylinder , charge on surface, why is B inside zero?

Suppose we have a cylindrical wire of radius a carrying a current I. If the current is uniformly distributed over the surface of the wire, the magnetic field inside is zero. We can prove that easily ...
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1answer
208 views

Where is F=BIL force exerted on my conductor?

In order to get to the formula $F=BIL$ (L is the length of a wire,B a steady magnetic field,I a constant current) we integrate with respect to dl from 0 up to the length L of the straight wire. So the ...
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3answers
5k views

Magnetic field along the axis of a solenoid - Can I find it this way?

I know how to find the magnetic field of a current carrying loop along its axis. The result is the following : $$B=\frac{μ_0IR^2}{2(R^2+z^2)^{3/2}}$$ z is the axis, R the distance of the loop from ...
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1answer
64 views

Differential element of current question

I'm watching some basic magnetic field derivations and most of the proofs use the differential element $dI$. Let's say a wire carries a current I. When we take a very small current $dI$ though , ...
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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
322 views

Calculate lorentz force on a surface?

I know the equation $$\vec F=q(\vec u\times\vec B)$$ If current I is flowing through a circular surface and that current creates a magnetic field in that surface what is the force F exerted on the ...
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1answer
302 views

Magnetic force in the inside of cylindrical conductor?

I'm trying to solve a problem and I can't actually understand what I need to find. I'll try translating in English hoping it will make some sense. We have a cylindrical conductor carrying a ...
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1answer
2k views

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
59 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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0answers
86 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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1answer
304 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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1answer
991 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 $\vec H$....
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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
203 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
80 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
436 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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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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2answers
3k views

Deriving Biot-Savart Law from Maxwell's Equations

As an exercise, I've been trying to derive the Biot-Savart law from the second set of Maxwell's equations for steady-state current $$\begin{align}&\nabla\cdot\mathbf{B}=0&&\nabla\times\...
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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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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}$...
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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
103 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
230 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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1answer
101 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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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
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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2answers
4k views

Ampère's law vs Biot Savart law

So I feel like I understand how both these laws work however it seems like Ampère's law will find the strength of the magnetic field at a point (the point is taken as $z$ in this example and the red ...
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1answer
579 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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3answers
2k views

Direction of electric dipole moment and magnetic dipole moment

For electric dipole: The direction of the dipole moment is from negative to positive charge, but that of the electrostatic field is from positive to negative. But in the case of magnetostatics, the ...
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1answer
449 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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1answer
830 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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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
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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 ...