# What is Magnetostatics: Definition and 77 Discussions

Magnetostatics is 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. The magnetization need not be static; the equations of magnetostatics can be used to predict fast magnetic switching events that occur on time scales of nanoseconds or less. Magnetostatics is even a good approximation when the currents are not static — as long as the currents do not alternate rapidly. Magnetostatics is widely used in applications of micromagnetics such as models of magnetic storage devices as in computer memory. Magnetostatic focussing can be achieved either by a permanent magnet or by passing current through a coil of wire whose axis coincides with the beam axis.

View More On Wikipedia.org
1. ### A Why is "method of image current" valid in magnetostatics?

Hi wise folks, I am working through Jackson problems, and have just encountered problem 5.17: It is pretty straightforward to show that the given image current distributions will satisfy the boundary conditions (both tangent and normal) at the ##z=0## plane. But my question is actually: "why...
2. ### I Biological examples of a Biot-Savart law in magnetostatics?

Hello everyone, So, I was wondering, the Biot-savart show us a magnetic field created by a constant electric current. Initially I thought that an example would be biological systems with a nervous system that works on the basis of electrical discharges, but I don't think it's a valid example...
3. ### Derivation of torque on general current distribution

How do I simplify the expression...
4. ### Finding the magnetic field B given the vector potential A ?

hi guys this seems like a simple problem but i am stuck reaching the final form as requested , the question is given the magnetic vector potential $$\vec{A} = \frac{\hat{\rho}}{\rho}\beta e^{[-kz+\frac{i\omega}{c}(nz-ct)]}$$ prove that $$B = (n/c + ik/\omega)(\hat{z}×\vec{E})$$ simple enough i...
5. ### E&M: Field of a Wire with non-uniform current

Summary:: Not sure if my solution to a magnetostatics problem is correct [Mentor Note -- thread moved from the technical forums, so no Homework Template is shown] I was trying to solve problem 2 from...
6. ### Understanding a step in a Biot-Savart law problem

I can't understand intuitively why the authors of the book expressed the cross product between the vectors dl and r (unit vector) as: dl sin(pi/2 - theta); isn't it supposed to be expressed as: dl sin(theta)?? So why did the authors put that pi/2 into the argument of sin function, that's my...
7. ### How to find the magnetic field and magnetic force due to a solenoid loop

I'm not so sure how to begin with this problem. I was thinking of usign superposition. I think that the field on the conductor due to the parallel segments of the coil is zero, since Ampere's Law tells us that the field outside the solenoid is zero, right? For the perpendicular segments, I used...
8. ### Magnetostatics and Ampere's law on a finite length wire

I tried to think why Ampere's law seems to fail in this case. For me it was clear that there is no symmetry in the z direction, there is no translational symmetry because of the finiteness of the wire. On the other hand, I know that Ampere's law is independent of the loop we take. This also...

10. ### What is the significance of neglecting the encircled sides in Ampere's law?

This is a very basic issue but really important as well. The rectangular loop has length ##l## and width ##h##. I have seen the argument of neglecting the encircled sides of the loop because ##h << 1## while using Ampere's law to calculate the magnetic field flowing over a plane. I find this...
11. ### Why am I getting Maxwell's second equation wrong?

While going through an article titled "Reflections in Maxwell's treatise" a misunderstanding popped out at page 227 and 228. Consider the following equations ##(23\ a)## and ##(23\ c)## in the article (avoiding the surface integral): ##\displaystyle \psi_m (\mathbf{r})=-\dfrac{1}{4 \pi} \int_V...
12. ### A magnetostatics problem of interest 2

A very important problem in magnetostatics is the uniformly magnetized cylinder of finite length. Permanent cylindrical magnets can be modeled as having approximately uniform magnetization, and it is of much interest, given such a uniformly magnetized cylinder, to be able to calculate the...
13. ### I Showing that B has no discontinuities at the surface

Consider a magnetic dipole distribution in space having magnetization ##\mathbf{M}##. The potential at any point is given by: ##\displaystyle\psi=\dfrac{\mu_0}{4 \pi} \int_{V'} \dfrac{ \rho}{|\mathbf{r}-\mathbf{r'}|} dV' + \dfrac{\mu_0}{4 \pi} \oint_{S'}...
14. ### Why the magnetic field doesn't have to describe a circle?

Homework Statement Imagine an infinite straight wire pointing at you (thus, the magnetic field curls counterclockwise from your perspective). Such a magnetic field equals to: $$B = \frac{\mu I}{2 \pi s} \hat{\phi}$$ I want to calculate the line integral of ##B## around the circular path of...
15. ### Find the magnetic field inside the cylinder

Homework Statement There's a very long cylinder with radius ##R## and magnetic permeability ##\mu##. The cylinder is placed in uniform magnetic field ##B_{0}## pointed perpendicularly to the axis of cylinder. Find magnetic field for ##r < R##. Assume there's a vacuum outside the cylinder...
16. ### The speed of a metal wire on two rails with a magnetic field

Homework Statement I tried to understand the problem b) and c).[/B] Homework Equations Faraday's law: ∇xE = - ∂B/∂t emf ε = Bdv Force : F =ma, Lorenz's force F=q(vxB) ==> ma = IdB Power : power of battery = εI, mechanical power of the wire = Fv The Attempt at a Solution I think I solved...
17. ### Toroid with Air Gap magnetostatics problem

Homework Statement consider a toroidal electromagnet with an iron ring threaded through the turns of wire. The ring is not complete and has a narrow parallel-sided air gap of thickness d. The iron has a constant magnetization of magnitude M in the azimuthal direction. Use Ampere's law in terms...
18. ### Electromagnetism Help-- Magnetostatics Boundary Problem

Homework Statement Two magnetic materials are separated by a planar boundary. The first magnetic material has a relative permeability μr2=2; the second material has a relative permeability μr2=3. A magnetic field of magnitude B1= 4 T exists within the first material. The boundary is...
19. ### Magnetic field in the case of a thin magnetized cylinder

Homework Statement Consider a cylinder of thickness a=1 mm and radius R = 1 cm that is uniformly magnetized across z axis being its magnetization M= 10^5 A./m. Calculate the bound currents on the cylinder and, doing convenient approximations, the B field on the axis of the cylinder for z=0...

22. ### Direction of the magnetic field around a solenoid

Homework Statement Example 5.9 in Griffiths's Introduction to Electrodynamics 4th shows us how to find B of a very long solenoid, consisting of n closely wound turns per unit length on a cylinder of radius R, each carrying a steady current I. In the solution, he goes on to explain why we don't...
23. ### Magnetostatics experiment flowchart - How can I improve this

Homework Statement I'm attempting to write a FORTRAN program that calcuates the magnetic field, B, at any point outside of a bar magnet. I will be using a simple first order euler scheme for numerical surface integration. Homework Equations Here is the exact method I will be using...
24. ### B on center of 2 infinite wires with semi - circular end

Homework Statement Homework EquationsThe Attempt at a SolutionMagnetic field due to both semi - infinite straight wires on P = Magnetic field due to infinite straight wire on P = ## \frac { \mu_0 I } { 2 \pi a } = 2 * 10 ^{-5} ~wb/m^2 ## Magnetic field due to semi – circular wire on...
25. ### Magnetostatics - Magnetic field of a nonuniform current slab

Homework Statement A thick slab in the region 0 \leq z \leq a , and infinite in xy plane carries a current density \vec{J} = Jz\hat{x} . Find the magnetic field as a function of z, both inside and outside the slab. Homework Equations Ampere's Law: \oint \vec{B} \cdot d\vec{l} = \mu_0...
26. ### Magnetic field above the center of a square current loop

Homework Statement Find the exact magnetic field a distance z above the center of a square loop of side w, carrying a current I. Verify that it reduces to the field of a dipole, with the appropriate dipole moment, when z >> w. Homework Equations (1) dB = μ0I/4πr2 dl × rhat (2) r =...
27. ### Radial force on charged particle in beam of positive ions

Homework Statement Many experiments in physics call for a beam of charged particles. The stability and “optics” of charged-particle beams are influenced by the electric and magnetic forces that the individual charged particles in the beam exert on one another. Consider a beam of positively...
28. ### I 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## where ##p## is pole strength in emu In SI units: ##F_{N}=k_A \dfrac{P^2}{r_m^2}=10^{-7}...
29. ### Jackson's 6.4 - Uniformly magnetized conducting sphere

Homework Statement A uniformly magnetized and conducting sphere of radius R and total magnetic moment m = 4\pi MR^3/3 rotates about its magnetization axis with angular speed \omega. In the steady state no current flows in the conductor. The motion is nonrelativistic; the sphere has no excess...
30. ### Magnetic field behind “invisible barrier”

Let us consider the following thought experiment. There is a magnetic field in free space produced by a steady current, hence solution of the (magnetostatic) Ampere's law Curl H = J. There is also a material with some parameters ε and μ and no currents, where the Ampere's law is Curl H = 0...
31. ### Can stationary permanent magnet do work?

We have a permanent saturated magnet. And a coil wound around it. The current produces magnetic field in same direction as the magnet. Now we know that the energy of magnetic field is proportional to the square of the magnetic induction. E1=kB12 E2=kB22 Etotal=kB12+kB22+2kB1B2 We have an extra...
32. ### Can we define a circular loop with moving electrons as magnetostatic?

When I learned magnetostatics. My teacher and book said that it is the case of steady current. However, if I consider a circular loop, the electrons are in fact moving in uniform circular motion. That means they are accelerating. How come we can still define it to be a magnetostatic situation
33. ### Magnetostatics force equation for continuous current density

In Jackson, the following equations for the vector potential, magnetostatic force and torque are derived##\mathbf{m} = \frac{1}{{2}} \int \mathbf{x}' \times \mathbf{J}(\mathbf{x}') d^3 x'## ##\mathbf{A} = \frac{\mu_0}{4\pi} \frac{\mathbf{m} \times \mathbf{x}}{\left\lvert {\mathbf{x}}...
34. ### Magnetostatics: What if "steady" currents were divergent?

Why must steady currents be non-divergent in magnetostatics? Based on an article by Kirk T. McDonald (http://www.physics.princeton.edu/~mcdonald/examples/current.pdf), it appears that the answer is that by extrapolating the linear time dependence of the charge density from a constant divergence...
35. ### Magnetic Mirror for Neutral Atoms

Homework Statement Consider an infinite sheet of magnetized tape in the x-z plane with a nonuniform periodic magnetization M = cos(2πx/λ), where λ/2 is the distance between the north and south poles of the magnetization along the x-axis. The region outside the tape is a vacuum with no currents...
36. ### Determining the force on a loop cause by an infinite line

Homework Statement An infinitely long line of current $I_1=6[A]$ is following along the positive z-axis in the direction of +$\hat{a_z}$. Another current is following a triangular loop counter clockwise from the points A(0,2,2), B(0,6,2) and C(0,6,6). Homework Equations To start I applied...
37. ### Calculate pressure difference in current-carrying mercury

Homework Statement A vertical column of mercury, of cross-sectional area A, is contained in an insulating cylinder and carries a current I0, with uniform current density. By considering the column to be a series of concentric current carrying cylin- ders, derive an expression for the...
38. ### Engineering Deriving the circuit approximation of a magnetic circuit

Homework Statement For the magnetic circuit: Derive the circuit approximation. Compute all magnetic fluxes if the total solenoid current is I. Homework Equations Rm = L / μS The Attempt at a Solution [/B] Mostly, right now, I'm just trying to determine the magnetic circuit equivalent. From...
39. ### Vector Potential: Infinite Wire and Infinite Solenoid

Homework Statement Homework Equations Provided in the questions I believe. Here's the triangle from question two. The Attempt at a Solution QUESTION SET 1 TOP OF PICTURE A.) I didn't know how to just "guess" what the constant should be so I actually worked it out. I found the constant...
40. ### Finding the Delta Function of a Thin Ring

Homework Statement [/B] A very thin plastic ring (radius R) has a constant linear charge density, and total charge Q. The ring spins at angular velocity \omega about its center (which is the origin). What is the current I, in terms of given quantities? What is the volume current density J in...
41. ### Magnetic moment between 2 bar magnets

Homework Statement A bar magnet floats above another bar magnet. The first has mass u1 and magnetic moment m1=m1k^ and is on the ground. The second has mass u2 and mag. moment m2=-m2k^ and is a distance z above the ground, find z 2. Homework Equations I assume I need to calculate the magnetic...
42. ### On the Pole Method of Magnetostatics and Permanent Magnets

The pole method of magnetostatics is presented in many E&M textbooks, particularly the older ones, to do computations in magnetostatics and even to try to explain permanent magnets. An equation that arises in the pole method is B=H+4*pi*M (c.g.s. units), where H consists of contributions...
43. ### Magnetostatics: Finding B field using Amperes Circuital Law

I am preparing for an exam and I am going through a past paper which has solutions given for the questions but I need help understanding how the answer comes about. I suspect it may be just the algebra I don't get, but it may be the physics too. Wasn't sure if this was the correct forum either...
44. ### Work and Heat Transfer in a Magnetic Field: Conduction Rod on Conducting Rails

Homework Statement A conduction rod (of mass ##m## and length ##l##) was placed on two smooth conducting rails rails connected by a resistor as shown: (the circuit is placed in ##XY##-plane A constant uniform magnetic field is switched on along ##-Z## direction with magnitude ##B## The rod is...
45. ### Finding B, M, and H for an infinite conducting slab

Homework Statement We have an infinite slab of conducting material, parallel to the xy plane, between z = −a and z = +a, with magnetic susceptibility χm. It carries a free current with volume current density J = J0z/a in the x direction (positive for z > 0, negative for z < 0). The integrated...
46. ### Magnetostatics: Finding B field given current density

Homework Statement Not sure if this is the correct place to post so move if needed. In a cylindrical conductor of radius R, the current density is givne by j_0 e^{- \alpha r} \hat{k}. Where ##\alpha## and ##j_0## are some constants and ##\hat{k}## is the unit vector along the z-axis. ...
47. ### Prove that the torque of any current loop is m X B

Homework Statement Problem 6.2 of Griffith's "Introduction to Electrodynamics": Starting from the Lorentz force law ##\vec F=\int I (d\vec l \times \vec B)##, show that the torque on any steady current distribution (not just a square loop) in a uniform field ##\vec B## is ##\vec m\times \vec...
48. ### Why is it advantageous to use vectors D and A in problems?

At the moment we are working through problems in Griffiths' Electrodynamics textbook and it got me thinking... In magnetostatics we have the magnetic vector potential A and in the use of dielectrics problems we have the vector D. Why is it advantageous to use these vectors and not just stick to...
49. ### Current distribution, magnetostatics

Homework Statement If we want to obtain a magnetic dipole in the interior of a sphere of a radius R, what should be the current distribution over the surface of the sphere? Note that its permeability is the one of the vacuum. Determine the magnetic field outside the sphere. Homework...
50. ### Thide's treatment of magnetostatics

Hi all, I've been having a look at Thidé's treatment of magnetostatics in the free ebook www.plasma.uu.se/CED/Book/EMFT_Book.pdf A couple of questions, about embarrassingly simple matters that I've forgotten: 1) In equation (1.11), is it a mistake that the magnetic force between two...