Magnetostatics Definition and 76 Threads

The bound surface current is $$\mathbf{K}_b = \mathbf{M} \times \hat{n}$$ which gives $$\mathbf{K}_b = {M} \hat{x}$$ Applying ampere's law: ##\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{\text{enc}}## to the top surface, which encloses the bound surface current yields: ##\mathbf{B} = \mu_0...

My final result was $$\tau = IBR\sin{\theta} \int_{0}^{2\pi} {\frac{\sqrt{1+\sin^2{\theta}\cos^2{\gamma}}}{\sqrt{1+\sin^2{\theta}\cos^2{\gamma}}}d\gamma}$$. I think I am supposed to get a simple answer like $$\tau = \vec{\mu} \times \vec{B}$$ where mu=IA. If I take approximations using the...

I can't see what is the problem with my derivation but the answer is incorrect. Please help. We assume here that ##\omega_0 = 0## and ##v_0 = 0##, hence it immediately rolls without slipping without any transitional phase. Hence ##v = \omega R##. Thus, ##v(L) = R\omega(L)##. Since our...

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...

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...

How do I simplify the expression...

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...

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...

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...

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...

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...

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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...

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...

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...

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'}...

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...

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...

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...

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...

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...

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...

Homework Statement This is from Griffith's Introduction to Electrodynamics, where the book is deriving the magnetic dipole moment from multipole expansion of the vector potential The vector potential of a current loop can be written as $$\mathbf{A(r)}=\frac{\mu_0 I}{4\pi} \left[ \frac{1}{r}...

In his book on EM, Griffiths states: Formally, electro/magnetostatics is the régime $$\frac{\partial \rho}{\partial t}=0, \hspace{0.25in} \frac{\partial \vec{\boldsymbol{J}}}{\partial t}=\boldsymbol{0}$$ He explains how in electrostatics charges do not move, or (more specifically), charge...

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...

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...

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...

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 =...

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...

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}...

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...

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...

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...

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

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}}...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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. ...

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...

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...

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...