What is Ampere's law: Definition and 213 Discussions

In classical electromagnetism, Ampère's circuital law (not to be confused with Ampère's force law that André-Marie Ampère discovered in 1823) relates the integrated magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell (not Ampère) derived it using hydrodynamics in his 1861 published paper "On Physical Lines of Force" In 1865 he generalized the equation to apply to time-varying currents by adding the displacement current term, resulting in the modern form of the law, sometimes called the Ampère–Maxwell law, which is one of Maxwell's equations which form the basis of classical electromagnetism.

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  1. oogleshmoogle

    When do I use Biot-Savart Law vs. Ampere's Law?

    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...
  2. DavideGenoa

    I Relaxed conditions for the density: Ampère's law still valid?

    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...
  3. T

    The Conditions for Biot-Savart Law to Ampere's Law

    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?
  4. PhiowPhi

    Ampere's law for a larger diameter?

    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...
  5. PhotonSSBM

    Justifying Ampere's Law and Faradays Law with an experiment

    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...
  6. DavideGenoa

    Commutations and delta in deriving Ampère's law

    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...
  7. DavideGenoa

    Commutation integral/derivative in deriving Ampère's law

    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...
  8. xareu

    Doubts on Ampère's Law and Coaxial Cables

    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...
  9. DavideGenoa

    Biot-Savart law from Ampère's (with multivariate calculus)

    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...
  10. S

    Ampere's law with current loop

    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...
  11. K

    Problem involving Ampere's Law and Understanding

    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...
  12. G

    Something wrong with Ampere's Law?

    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...
  13. M

    Calculate Magnetic field using Ampère's law

    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...
  14. T

    How Does Ampere's Law Account for Changes in Magnetic Field Strength?

    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...
  15. Nathanael

    Biot-Savart law and Ampere's law

    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...
  16. B

    Flow of Magnetic Charge: A Source in Ampere's Law? - Bob Eisenberg

    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
  17. kelvin490

    Ampere's law and magnetic circuit

    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...
  18. kostoglotov

    Line Integral/Ampere's Law: is my logic valid?

    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...
  19. Aavatar

    Magnetic Field of a rotating Cylinder

    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...
  20. N

    Integral Form of Gauss' Law at Center of Finite Wire

    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...
  21. S

    Ampere's Law - finding Magnetic Field

    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...
  22. endiewibowo

    How to calculate mutual inductance of a rectangular loop

    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...
  23. S

    Ampere's Law for a finite wire

    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...
  24. R

    Ampere's law in differential form

    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...
  25. J

    Ampere's Law and charge on the capacitor

    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...
  26. T

    Ampere's law and induced current

    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)...
  27. kelvin490

    Can Ampere's law be applied to 3D loop?

    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...
  28. Essence

    Using ampere's law for a circular loop

    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...
  29. jbenson

    Ampere's Law & Faraday's Law: Exploring Electromagnetic Wave

    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...
  30. S

    What does B.dl indicate in Ampere's Law

    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} ## = ??
  31. deedsy

    Magnetic Field inside plate

    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...
  32. Hijaz Aslam

    Magnetic Field using Ampere's Law

    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...
  33. W

    Derive Ampere's law from Biot-Savart law?

    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?
  34. arpon

    Calculating Magnetic Field in a Square with Varying Resistances

    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...
  35. arpon

    Problems about Ampere's Law and Biot-Savart's Law

    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...
  36. G

    Finding the magnetic field of an infinite cylindrical wire.

    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...
  37. W

    Ampere's Law - Showing that B at center is due only to wire

    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...
  38. DivergentSpectrum

    Can someone please explain Ampere's law to me?

    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"?
  39. F

    Deriving Ampere's law from the Biot-Savart law

    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...
  40. T

    Ampere's Law and Conductor: Finding ∫B.dl for a Semicircle in the x-z Plane

    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...
  41. B

    Ampere's Law Application Problem

    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...
  42. D

    Ampere's law for a point charge

    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...
  43. T

    Ampere's Law - Magnetic Field Strength

    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...
  44. R

    Ampere's Law when applied to a toroid

    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...
  45. Saitama

    Solving Ampere's Law Problem: Find Magnitude of B·dl

    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...
  46. D

    Ap physics c ampere's law and biot-savart

    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
  47. E

    Ampere's Law: A Clear Definition

    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 :)
  48. Mr-R

    Problem with Understanding Ampere's Law

    Dear all, I am trying use Ampere's law and came across a problem which is a result of my lack of understanding. \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 the line...
  49. S

    Biot-Savart law and Ampere's law

    1. An electric circuit consists of two long straight sections connecting a loop of radius r. The gap in the loop where the straight sections are connected subtends an angle of theta=60d, as shown in this figure (http://imgur.com/tseDHL6). Determine the magnetic field B at the point P in the...
  50. A

    Integrals over vector fields and Ampere's Law

    Homework Statement Experiments show that a steady current I in a long wire produces a magnetic field B that is tangent to any circle in the plane perpendicular to the wire and whose center is the axis of the wire. Ampere's Law relates the electric current to its magnetic effects and states...
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