# Questions tagged [magnetostatics]

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### 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 ...
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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### 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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### 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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### 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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### 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 ...
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 ...
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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### 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{...
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 ...
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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### 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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### 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 ...
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 ...
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 ...
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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### 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 ...
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 , ...
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(...
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 ...
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 ...
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 ...
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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### 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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### 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 ...
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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### 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 $\vec H$....
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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### 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 ...
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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### 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 ...
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 ...
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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### 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 ...
1k views