Ampere's law Definition and 211 Threads

Homework Statement Consider a two-layered cylindrical wire with inner-layer permeability μ1 and outer-layer permeability μ2. A line current I runs through the center in the z direction. Calculate the bound currents and the magnetic field produced by the bound currents. Homework Equations [1]...

I know the ampere's law but I want an explanation on why it exist in that way, consider a wire where flows current, i know that when an observer is in relative motion to the current there is a magnetic field but why in this geometric configuration and not in another? What about the electric...

This isn't a homework problem, I have the solutions for this problem. I'm just wondering why, for question 3, letter a, part ii, it's necessary to use the Biot-Savart law instead of Ampere's law? What are the use cases for Biot-Savart law vs. Ampere's law...

The most common proof that I have found of the fact that Ampère's law is entailed by the Biot-Savart law essentially uses the fact that, if ##\boldsymbol{J}:\mathbb{R}^3\to\mathbb{R}^3##, ##\boldsymbol{J}\in C_c^2(\mathbb{R}^3)##, is a compactly supported twice continuously differentiable field...

Mathematically, what conditions must a B-field that obeys the Biot-Savart Law satisfy before it will obey Ampere's Law? Additionally, what conditions must the B-field obey in order to satisfy Faraday's Law?

Most of the problems I've worked on involve wires of small radii, however, if DC current flows within large radii of conductive wires, would I need to use current density ##J## for calculating the magnetic field at a point ## r > R## instead of ##I## if it we're known? With relevance to a wires...

Homework Statement Given Ampere's Law and Faraday's Law (in differential or integral form fwiw) explain why it is easier to design an experiment to show that a changing magnetic field creates an electric field than it is to show a changing electric field creates a magnetic field. Justify your...

Hi, friends! I have been able to understand, thanks to Hawkeye18, whom I thank again, that, if ##\mathbf{J}## is measurable according to the usual ##\mathbb{R}^3## Lebesgue measure ##\mu_{\mathbf{l}}## and bounded, a reasonable hypothesis if we consider it the density of current, if...

Hi, friends! I have been struggling to understand the only derivation of Ampère's law from the Biot-Savart law for a tridimensional distribution of current that I have been able to find, i.e. Wikipedia's outline of proof, for more than a month with no result. I have also been looking for a proof...

I have a doubt about Ampère's that keeps me awake at night haha, but I think that for a more knowledgeable person it may seem pretty obvious. I've seen in several books that, in a coaxial cable with equal and opposed currents in the core and shield, the magnetic field outside the outer conductor...

Let us assume the validity of Ampère's circuital law\oint_{\gamma}\mathbf{B}\cdot d\mathbf{x}=\mu_0 I_{\text{linked}}where ##\mathbf{B}## is the magnetic field, ##\gamma## a closed path linking the current of intensity ##I_{\text{linked}}##. All the derivations of the Biot-Savart law for a...

Is it possible to find the magnetic field on the axis above a current loop using Ampere's law? I was thinking you could treat an infinitesimal piece of the loop as a straight wire and draw a circle around it with radius sqrt(a^2 + z^2), with a=radius of current loop and z=position of point of...

Homework Statement Hello, This is a multi-part problem but I am stuck on just the third part, but I am a little confused in general with Ampere's Law. I know that the equation is mu_0*Ienc=Integral of B dl, but this problem really confused me. A long straight copper wire lies along the z...

We use ∇ x B = μ0 J Imagine a thin metal wire. We measure the curl at some distance from the wire and from the Biot-Savart law we know that it is not zero. However, as this point is at some distance from the wire, the current density at that point is definitely zero. I'm confused as to why...

Homework Statement I have an assignement in school. The statement is: chose a distribution of electric curents for which you can calculate easily the magnetic field (for example, using Ampère's law). Describe your distribution and explain the way you calculate the magnetic field. Homework...

hello everybody! I have a problem with ampere's low.assume that we have an iron core with a winding in on side of it as sketched in the below image.we want to find H(magnetic field strength) and B(magnetic flux density) in the core in different condition shown in the right of image .the...

If we integrate the magnetic field from the Biot-Savart law for an infinitely long straight wire, we can get ##|B|=\frac{\mu_0 i}{2\pi R}## with R being the shortest distance from the wire to the point in space. If we use Ampere's law (with a circle of radius R centered on a wire with the...

If magnetic charge exists, it can flow. Would the flow of magnetic charge produce a current that would be a source for the curl of B, in Ampere's law? Ever yours Bob Eisenberg Chairman emeritus Dept of Molecular Biophysics Rush University Medical Center

For magnetic circuit there is an equation NI=HL. This equation is obtained by applying Ampere's law. H is magnetic field intensity and L is the length of the circuit. In following picture the equation reduced to I=HL as there is only one turn...

This is a problem from a section on Line Integrals in my Calculus Textbook, I haven't studied any physics relating to E&M yet, and the solutions manual only gives solutions for odd numbered problems. Sorry, if I'm posting in the wrong forum, I hope I'm not. 1. Homework Statement A steady...

Homework Statement .[/B] Given an infinitely long charged metal cylinder that is rotating with an angular velocity ##\omega## The charge density per unit length is ##\rho##. Find the magnetic field within the cylinder. I'm trying to solve this problem by using Ampere's Law. But couldn't reach...

At the exact center of a finite wire (i.e. a distance, say $L/2$ from each end), why can I not apply Gauss's Law in integral form to find an EXACT solution for the electric field? At the center of the wire, $E$ is entirely radial, so it seems like I should be able to draw an infinitesimally...

Homework Statement A long, straight, cylindrical conductor with relative permeability ## \mu ## has a radius a and carries a current I. The current density is uniform. Using Ampere's law in it's integral version, finding the magnetic field B: a) Inside, and b) outside the cylinder. Homework...

I am planning to build a rogowski coil but not the conventional one, which is a circular loop. Below is the example of a rogowski coil so you have the big picture of my question. In the picture, the current conducting wire (with current Ip) is encircled by a big circular loop rogowski coil...

Greetings, I am working as a TA and I encountered a particular question which asks the student to use the Ampere's Law in order to get the magnetic field created by a semi-infinite wire. I know that there will be charge accumulation a time-dependent electric-field, hence a displacement current...

Homework Statement A long cylindrical wire of radius R0 lies in the z-axis and carries a current density given by: ##j(r)= j_0 \left( \frac{r}{R_0} \right)^2 \ \hat{z} \ for \ r< R_0## ##j(r) = 0 \ elsewhere## Use the differential form of Ampere's law to calculate the magnetic field B inside...

Homework Statement Number 9 Homework Equations Ampere's law; B*dl= mu(I_enclosed + I_displace) I_displace=e_0 * d(E*dA)/dt The Attempt at a Solution [/B] There's no current enclosed, only displacement current. I don't know how to find the change in electric flux, so I don't know how I...

Homework Statement Homework Equations ∫BdL = μI The Attempt at a Solution a) the magnetic field is a circle around the wire so the length of the path is the circumference of the circle which is 2πr ∫BdL = BL = μI B(2πr) = μI B = μI/2πr in this problem it is into the page (right hand rule)...

Usually in textbooks Ampere's law is just illustrated using 2D loops which forms a plane. Can the law be applied to 3D loops which cannot form a plane surface within the loop? In a 3D loop which surface should we count when we count the current? In 2D case it is easy because there can only be a...

Homework Statement Sorry to bother you guys, I've heard that Ampere's Law is either ineffective for calculating the B field due to a circular loop or needs some modification (I wasn't sure which). I'm trying to figure out why this doesn't work so I can get a better understanding of Ampere's...

First, some background. In Faraday's law the reluctance/resistance by "mother nature" to changing the magnetic flux is explicitly recognized by the "-" sign (commonly referred to as Lenz's law), i.e. if the time rate of change of the magnetic flux is positive, an emf is induced so as to oppose...

I know that \oint \vec E \cdot \vec{dS} in Gauss Law indicates electric flux. \oint \vec E \cdot \vec{dS} = \frac{Q_{enc}}{\varepsilon_0} But what does B.dl indicate in Ampere's Law? ##\oint \vec{B} \cdot \vec{dl} ## = ??

Homework Statement What is the magnetic field outside and inside of a large, flat conducting plate if the current density decreases linearly with depth z inside the plate. J = J0(1-az). The plate thickness is 1/a. Homework Equations *see below The Attempt at a Solution \oint \vec B \cdot d...

I find Ampere's Circuital Law sort of fishy. I don't understand what the actual theory proposes. And the loop that should be taken into consideration adds much to the confusion. How should we select the loop? And in the case of a long wire we find the magnetic field around it by applying...

In Serway physics, ampere derived Ampere's law(integral B dot ds=uI) with work done on the magnetic charge by magnetic field.(similear with E dot ds) Without using vector calculus, how can derive Ampere's law from Biot-Savart law?

Homework Statement [/B] Consider a square whose successive sides of length L has resistances R, 2R, 2R, R respectively. If a potential difference V is applied between the points (call them , say , A and B) where the sides with R and 2R meet. Find the magnetic field B at the center of the...

Suppose there is a potential difference between points A and B which are connected by a straight wire. The current in AB is i. We want to calculate the magnetic field at point C which is at distance r from the middle point P of the wire and CP is perpendicular to AB. At first, we use Ampere's...

Homework Statement An infinite cylindrical wire of radius ##R## carries a current per unit area ##\vec{J}## which varies with the distance from the axis as ##J(s)=ks^2\hat{z}## for ##0<s<R## and zero otherwise where k is a constant. Find the magnetic field ##\vec{B(s)}## in all space. Homework...

Homework Statement In Fig. 29-71, a long circular pipe with outside radius R = 2.6 cm carries a (uniformly distributed) current i = 8.00 mA into the page.A wire runs parallel to the pipe at a distance of 3.00R from center to center. Find the (a) magnitude and (b) direction (into or out of the...

The closed line integral of the B field equals m*I where m is permeability and I is the current enclosed. Does this mean amperes law only holds for infinitesimal current elements (or a moving charge?) Because how else can a current be "enclosed"?

If we write the Biot Savart law as B(r)=μ0/4π∫(J(r')xn/n2)dV' where B is the magnetic field which depends on r=(x,y,z), a fixed point, J is the volume current density depending on r'=(x',y',z'), and n=r-r', a vector from the volume element dV' at r' to the point r. Note we integrate over the...

Homework Statement A conductor carrying current ‘I’ is in the form of a semicircle AB of radius ‘R’ and lying in the x-y plane with its centre at origin as shown in the figure. Find the magnitude of ∫B.dl for the circle 3x2 +3z2 =R2 in the x-z plane due to curve AB. Ans (1-√3/2)μ0I Homework...

Homework Statement I want to know why the book says that when ρ>c, there is no current and the magnetic will be zero Homework Equations Hø=I/2∏ρ The Attempt at a Solution I was trying to find the magnetic between the gap by using the formula... I've found that the magnetic magnetic...

I'm having some trouble confirming Ampere's law for a moving point charge. Let's say we have a point charge q moving with velocity \mathbf{v}. The magnetic field it creates is given by \mathbf{B}=\frac{\mu_0 q}{4\pi r^3} \mathbf{v}\times \mathbf {r}. Now consider a circular loop centred...

Homework Statement Use Ampere's Law to show that the magnetic field strength at a distance R from a long, straight wire, carrying a current I, is: H = I/2\piR Homework Equations F=qVB B=\mu0I/2\piR The Attempt at a Solution I'm not sure how to answer this question. I got the...

It's a simple question: Why is Ienc in Ampere's Law in a toroid equal to µ0NI where N is the number of loops around the toroid? Why is I N times greater when the wire is looped around the toroid? When you take a random wire with current and you change the geometry of the wire into a loop...

Homework Statement A conductor carrying current ##I## is in the form of a semicircle AB of radius ##R## and lying in xy-plane with it’s centre at origin as shown in the figure. Find the magnitude of ##\oint \vec{B}\cdot \vec{dl}## for the circle ##3x^2+3z^2=R^2## in the xz plane due to curve...

For AP Physics C level, I am having trouble on deciding whether to use Ampere's Law or use Biot-Savart. Are there any hints/tricks for deciding what to use? For example, in solenoids i heard it's easiest to use Ampere's Law

Could someone give me a word definition of Ampere's Law as I have googled some definitions and they all seem a bit confusing. Thanks :)

Dear all, I am trying use Ampere's law and came across a problem which is a result of my lack of understanding. [SIZE="4"]\oint B.dl=uI My lecturer derived the above equation by defining a point in the middle of a potato shaped loop. Where he stated that dl in this case is just rdθ. (r is...