Questions tagged [magnetostatics]

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Does zero free current entail zero $\vec H$?

There are two kinds of magnetic fields (different authors give them different names), $\vec B $ and $\vec H$ which are related by the equation $$ \vec B = \mu_o (\vec H + \vec M)$$ where $\vec M$ is ...
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2answers
615 views

Challenging Magnetostatics Problem - the “blind spot” of a magnetic dipole

I'm reviewing for an electromag exam and I stumbled upon a problem that's really hard to figure out. Here it is: A small magnetic dipole with moment $\vec m = m_o \hat z$ is in a region with uniform ...
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2answers
623 views

Energy density of magnetostatic fields

Consider that we are given magnetostatic field $B=B_1$ and $\frac{dB}{dt}=0$ from the beginning of time to the end of time. We are interested in the potential energy contained in the field. We know ...
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1answer
436 views

What are the advantages of Magnetocardiography?

I am reading the book Bioelectromagnetism by Malmivuo: Difference between the bioelectric and biomagnetic measurements lies in the sensitivity distributions of these methods. Diverse technical ...
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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{...
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2answers
165 views

Electromagnetic Theory [closed]

As, using the fact that E*A stays constant for a point charge ( E= electric field, A=area of sphere centered on charge touching the point where we have to measure E) , we can prove that E falls by 1/...
2
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1answer
138 views

What is the physical basis of the $\rho \bf{u} \times \bf{\omega}$ force on a fluid vortex line?

In fluid dynamics, the force density on a vortex line is $\bf{f} = \rho \bf{u} \times \bf{\omega}$. In Faber, Fluid Dynamics for Physicists, ch. 4, this is "derived" by analogy with magnetostatics, ...
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1answer
4k views

Ampere's circuital law for finite current carrying wire

When I was studying about Ampere's circuital law. Then there comes a question in my mind that "whether this law is applicable for finite current carrying wire or not"
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1answer
98 views

Force between two current carrying wires

Is the force which acts perpendicular to a wire due to another current wire in its vicinity consistent or it is just for a brief time? I thought it should be for a brief time because only for a moment ...
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2answers
584 views

Velocity of a Charged particle in a magnetic field according to Biot-Savart Law

According to Biot-Savart Law, if there is a charged particle in motion, there will be a magnetic field. My question is whether the counterpart of this law also holds true, i.e. if there is a magnetic ...
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1answer
981 views

quadrupole moment and higher for simple current loop

I'm working on a field configuration that needs to die off rapidly and I got to a $1/r^5$ dependence with canceling the dipole moment of the system cleverly, but to go get better arrangements I need ...
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2answers
663 views

How to express magnetic field vector in terms of force on current

I am preparing for an exam and one of the questions I have come across asks: Define the electric field $\mathbf{E}$ and the magnetic flux density $\mathbf{B}$, in terms of the force on charges and ...
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1answer
7k views

Magnetic field of uniformly charged rotating hollow sphere

I want to compute the magnetic field due to a homogeneously charged, rotating sphere with radius $R$, angular velocity $\vec{\omega} = \omega\hat{z}$ and total charge $Q$. I want to use Biot-Savart ...
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1answer
29k views

Magnetic field inside and outside cylinder with varying current density [closed]

I am reading through Introduction to Electrodynamics by David J. Griffiths and came across the following problem: A steady current $I$ flows down a long cylindrical wire of radius $a$. Find the ...
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2answers
531 views

Why does a solenoid's field look like this?

My book gives the above diagram but doesn't provide an explanation why the field looks like that. It simply says that the fields mostly cancel leaving the field above. Could someone walk me through ...
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1answer
154 views

Ampere's Law and Wires?

For a current carrying wire, the magnetic field $B$ is given by: $$B = \frac{u_oI}{2\pi r}$$ Is this only valid for a cylindrical wire?
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1answer
580 views

Ampere's Law and Circulation?

The net circulation should be zero if the net current is zero. However, I don't see how the circulation in the Amperian loop above can be zero. All the lines interact the loop only once and all their ...
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1answer
518 views

Assumptions when calculating $\vec{B}$ using Ampère's (circuital) law

When considering the same setup as in this question, i.e. a straight, infinitely long wire carrying the current $I$, Ampère's circuital law $$\oint_C \vec{B} \cdot \mathrm{d}\vec{r} = \mu_0 I_\text{...
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1answer
646 views

Which surface to use in Ampere's law?

In calculating the current enclosed by an Amperian loop, one must, in general evaluate an integral of the form $$I_\text{encl} = \int \mathbf{J}\cdot\mathrm{d}\mathbf{a}$$ The trouble is, there are ...
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1answer
2k views

Why use the method of images in magnetostatics?

If a current is above a conducting surface, why do we take the image of the current to find the magnetic field intensity? Why not just take the effect of the actual current only? And are this method ...
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3answers
583 views

Magnetic scalar potential far above a magnetic film

The situation I am looking at is a magneto-static problem of a finite magnetic film with magnetization $\bf{M}$. I would like to find the the magnetic field far above the plate. My expectation is that ...

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