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. A

    Deriving Magnetic Field Magnitude using Ampere's Law

    Homework Statement Ampere's Law states \int _C \vec{B} \cdot \vec{dr} = \mu_0 \ I . By taking C to be a circle with radius r, show that the magnitude B = |B| of the magnetic field at a distance r from the center of the wire is B = \frac{\mu_0}{2 \pi} \...
  2. S

    Magnetic fied at center of semicircle Ampere's Law Biot-Savart Law

    Homework Statement A long wire is bent into semicircle of radius R at its center and continues on to infinity in both direcions with the straight segments remaining parallel, as shown in the figure below. Use your knowledge of superposition, Ampere's Law, and the Biot-Savart Law to determine...
  3. Y

    Ampere's Law: Understanding Its Complexities

    I'm a bit confused on the exact workings of Ampere's law. Firstly, why does the shape of the Amperian loop not matter. Is there a mathematical proof that all Amperian loops are equivalent for the purpose of this law? Secondly, the law still holds valid in the presence of external magnetic...
  4. Y

    How Does Proximity of the Path Affect Ampere's Law Calculations in Solenoids?

    When deriving the formula for the magnetic field of a solenoid it is said that the side of the rectangle outside and parallel to the solenoid can be ignored because it is taken far away and the contributions of the field outside is negligible. But any arbitrary path can be taken and the...
  5. R

    Ampere's Law (enclosed current?)

    Hi, I was hoping someone could clarify Ampere's Law for me. The equation says that the only current that contributes to the magnetic field is current enclosed by the loop you select. But say you had a straight wire running through a solenoid, each having a current. If you selected a...
  6. E

    Solving Ampere's Law Homework Statement

    Homework Statement Homework Equations \int \vec B \cdot d\vecs = \mu i_{enc} The Attempt at a Solution This should be straight forward. I'm really starting to become frustrated with this textbook. Amperian Loop 1 encircles both current loops. \int \vec B \cdot d\vecs = \mu...
  7. T

    How Does Ampere's Law Apply to Conducting Wires and Cylindrical Shells?

    An infinitely long solid conducting wire of radius a = 2 cm centered on the z-axis carries a current I1 = 5 A out of the screen. The current is uniformly distributed over the cross-section of the wire. Co-axial with the wire is an infinitely long thin cylindrical conducting shell of radius of b...
  8. O

    Properly Applying Ampere's Law

    Homework Statement Different question, same problem. I edited this post from what I orignially posted it as (in which my issue was that I misread the problem). In Figure 29-63, a long circular pipe with outside radius R = 2.4 cm carries a (uniformly distributed) current i = 3.40 mA into the...
  9. N

    Ampere's Law: Find |H| at (6cm, 9cm, 0) in Toroid

    1. Homework Statement A toroid of a circular cross section whose center is at the origin and the axis the same as the z-axis has 1000 turns with po=10cm, a=1cm. If the toroid carries a 100mA current, find |H| at (6cm, 9cm, 0). 2. Homework Equations How do I calculate |H| at...
  10. N

    Can Ampere's Law Still Apply When Whole Solenoid Is Enclosed?

    Homework Statement I want to know why Ampere's Law can sitll be applied/valid if the Amperian surface is drawn as a rectangle which encloses a whole solenoid. Normally the rectangle would just include one side of the solenoid. Homework Equations The Attempt at a Solution When...
  11. I

    Ampere's Law (I think). Induced current from current carrying wire

    Homework Statement A 1.60 cm x 1.60 cm square loop of wire with resistance 1.10 \times 10^{-2} \Omega is parallel to a long straight wire. The near edge of the loop is 1.10 cm from the wire. The current in the wire is increasing at the rate of 100 A/s Homework Equations I think I have...
  12. L

    Ampere's law and biot-savort law

    stupid question - Why do we need Biot Savart law when we have ampere's law to determine the B field around a current carrying wire.
  13. L

    Ampere's Law and two conducting parallel plates

    hey sorry for the prolific posting but exam's are coming up and I'm just working through past papers. two conducting parallel plates have uniform uniform current densities flowing through them parallel to their surface. Use Ampere's Law to find the magnetic field inside and outside the...
  14. L

    Using Ampere's Law to Find Magnetic Field of Coil

    We have an infinite coil of N turns per unit length with radius a, carrying a current I and we want to find the magnetic field using Ampere's Law. If we put the loop outside the coil it can be established that B=0 If we use the loop to enclose the coil and we apply Ampere's Law we get that...
  15. L

    Understanding Ampere's Law: A Step-by-Step Derivation

    This must be a pretty standard proof but I'm having difficulty with part of it. So we have from Biot Savart law that \vec{B}(\vec{r})=\frac{\mu_0}{4 \pi} \int_V dV' \vec{J}(\vec{r'}) \times \nabla(\frac{1}{r}) we take the curl of this and show the second term vanishes to leave us with...
  16. C

    Solve Ampere's Law Problem for Uniform Current Density

    Homework Statement A conducting slab of thickness a is bounded by the planes z= \pma/2 and carries a uniform current density J=J (y hat) Use the integral form of Ampere's law to to find magnetic field everywhere 2. Relevant equations Integral for of Amperes law: Integral (B \bullet ds) =...
  17. J

    Am I on the right track with Ampere's Law?

    Homework Statement A wire carries a current of 3 A in the downward direction. What is the magnetic field 2.0 cm away from the wire? Homework Equations ∫B·dl = µ0I The Attempt at a Solution So I pick a circle with radius 2.0 cm to go around the wire, and get B∫dl = µ0(3 A) ∫dl...
  18. O

    Help with Ampere's Law: Toroid & Conducting Wire

    According to my textbook, the magnetic field of a toroid, according to ampere's law is given above as \frac{\mu_0{NI}}{2\pi{r}} but when i was looking through, I found that the magnetic field given by a piece of conducting wire is given as...
  19. F

    Ampére's Law Cylindrical Conductor with Hole

    Homework Statement A long circular rod of radius R, made of conducting material, has a cylindrical hole of radius a bored parallel to its axis and displaced from the centre of the rod by a distance d. The rod carries a current I distributed uniformly over its cross-section. Consider the...
  20. G

    Ampere's law, Biot-Savart law and E-field questions

    Hi, 1. Generally when using Gauss's law to e-field, I'm aware that the the surface you chose must be symmetrical and E-field is constant therefore you would only use Gauss's law for infinite sheets of charge, spherical distribution of charge and infinite line charge am i right? 2. Regarding...
  21. L

    Can Symmetry Arguments Simplify Ampere's Law for Solenoids?

    I need to use Ampere's Law and Gauss' Law to show that inside a solenoid B_r=0,B_\theta=0,B_z=0 i tried using cylindrical polars on ampere's law but the expression just got really long and i couldn't see any way out of it.
  22. S

    Using Ampere's Law to Calculate Magnetic Field at a Point

    Is there any way to use Ampere's Law \oint_{C}\beta d\ell = \mu_{0}I to calculate teh magnetic field \beta at a single point if there are no surfaces C such that \beta is constant over the surface's perimeter? Thanks Raman Edit: I mean solve symbolically, no estimation/splitting the integral...
  23. S

    Exploring Ampere's Law in a Radial Current Density Cylinder: Quick Test Prep

    Ampere's Law question (need quick answer test tomorrow) Using Ampere's Law on a solid cylindrical wire with radius R and a current density in the direction of the symmetry axis of the wire. The current density varies radially. J=J0*r^2. What is the magnitude of the the magnetic field when r>R...
  24. L

    Ampere's law and magnetic strength

    Homework Statement You have 16 m of 0.7 mm diameter copper wire and a battery capable of passing 21 A through the wire. What magnetic field strength could you obtain at the center of a single circular loop made from the wire? Homework Equations Ampere's law The Attempt at a Solution I...
  25. Z

    How Does Ampere's Law Determine the Ranking of Loops by Enclosed Current?

    Hellow every one I have small Q but I stuck on it there is pic attachedhope to be intersting and clear to you Homework Statement rank the loops accoroding to the current enclosed greatest first Homework Equations we have three eqn's B = u "node" I encِْْْْ B = u"node" i / 2 pi r...
  26. J

    Classical Electromagnetism: Question on Ampere's Law and Displacement Current

    Hi, just out of curiosity... Ampere's Law describes that an electric current produces a magnetic field. When corrected with Maxwell's displacement current, it describes that a magnetic field is also created by a time-varying electric field. Does this mean that an electric current produces...
  27. A

    Ampere's Law using the Biot Savart Law

    Is it possible to derive Ampere's Law(circuital) using the Biot Savart Law and elementary calculus? Thanks
  28. N

    How do I determine the direction of M and H in a homogeneous cylinder?

    Homework Statement Hi all. I'm trying to understand the H-field. From Ampére's law we have: \oint {{\bf{H}} \cdot {\rm{d}}{\bf{l}}} = I_{free,enclosed} If I look at an object with zero free, enclosed current, the integral equals zero. The integral can be equal to zero even if H is not zero...
  29. K

    How Does Integrating Magnetic Field in a Solenoid Result in BL?

    Why is it that integrating B ds gives BL where L is the length of the solenoid?
  30. K

    Ampere's law vs. Biot-Savart law

    What's the difference? Is Ampere's law a special case (when the conductor carrying the current is a straight wire?)
  31. K

    Ampere's law - single or double integral?

    Flux = Int B dA Why isn't this written as a double integral when we antidifferentiate over an areal?
  32. T

    Using ampere's law with current density

    K sorry for the bad drawing using paint...but anyways...so the question is :A long wire is in a conducting sheath and viewed from the top.The wire and the conducting sheath each carry opposite currents I into and out of the page with current density as J.The outer sheath has a radius of 2R and...
  33. K

    How Is Flux Calculated in a Toroid with Variable Radius?

    Homework Statement The question gives a coil of N turns carrying a current of I Amperes wound on a ring with rectangular cross section of inner radius r1 and outer radius r2 and height h. The ring has magnetic permeability mu. What is the flux in webbers? Homework Equations Ampere's Law...
  34. B

    Current Sheet - Ampere's Law

    Homework Statement Consider an infinite sheet of parallel wires. The sheet lies in the xy plane. A current I runs in the y-direction through each wire. there are N/a wires per unit length in the x direction. Write an expression for B(d) the magnetic field a distance d above the x y plane...
  35. S

    Calculating Magnetic Field of a Toroid Using Ampere's Law

    Use ampere's law to determine the magnetic field (a) inside and (b) outside a toroid, which is like a solenoid bent into the shape of a circle. Here is my work.. IS MY WORK CORRECT? a.) B(2PIr)=MoIenc and I found that B=MoNI/2pir b.) the magnetic field is 0 outside the loop
  36. M

    Ampere's Law and partial-circular wires.

    Why can't I use Ampere's law to compute the magnetic field at the center (P) of a semi-circular wire? If I calculate B at P due to d_theta, and then, using superposition, integrate from 0 to pi, the result is B=uI/2R. Biot-Savarte law gives the correct answer of B=uI/4R.
  37. J

    Understanding Ampere's Law: What Does the Current Enclosed Mean?

    Can anyone explain to me what Ampere's Law really is? For example, what does the current encircled really mean? Is it the total current passing through the loop in either direction?
  38. T

    Understanding Ampere's Law, Gauss's Law, and the Continuity Equation

    The Ampere's Law is \nabla \times B = \mu J and Gauss's Law is \nabla \cdot E = \frac{1}{\epsilon} \rho Since J is current density, is it right to say that, J = \frac{d}{dt} \rho in general? I am abit confused, since I know that a current four-vector, (\rho , J) is similar to a...
  39. L

    Independence of Gauss's law and Ampere's law

    Hi, I'm just learning about Maxwell's equations in high-school and was playing around with them. Supposedly they are 4 independent and self-sufficient equations that when connected with the Lorentz force law will predict classical electrodynamics in its entirety. But then, it appears to me...
  40. I

    Multiloop circuit, magnetic force on a current carrying wire, Ampere's Law

    1. Multiloop circuit In Fig. 27-71, R1 = 5.76 , R2 = 18.7 , and the ideal battery has emf = 13.8 V. (a) What is the size of current i1? http://img253.imageshack.us/img253/9926/fig2771dw3.gif Relevant equations i = V/R The attempt at a solution I redrew the 3 resistors (R2s) as...
  41. mbrmbrg

    Why is the position of the wire important for Ampere's Law to hold?

    Homework Statement A long straight cylindrical shell has an inner radius Ri and an outer radius Ro. It carries a current i, uniformly distributed over its cross section. A wire is parallel to the cylinder axis, in the hollow region (r < Ri). The magnetic field is zero everywhere outside the...
  42. S

    Solving Ampere's Law for Parallel Wires

    Homework Statement Calculate the magnitude of the magnetic field at a point midway between two long, parallel wires thar are 1.0 m apart and have currents of 10.0 A and 20.0 A, respectively, if the currents are: a) In opposite directions and b) in the same direction Homework Equations...
  43. J

    Why ampere's law cannot be applied to certain situations

    I know this question is asked a lot, but I am confused as to why ampere's law cannot be applied to certain situations. In particular: why can't it be used to calculate the field from a wire of finite length?
  44. F

    How Do You Determine the Distance a Proton Must Be from a Current-Carrying Wire?

    Homework Statement So a long straight wire lies on a horizontal table and carries a current of 1.2x10^-6A. In a vacuum, a proton moves parallel to the wire(opposite the current) with a constant speed of 2.3x10^4 m/s at a distance d above the wire. Determine the value of d. You may ignore...
  45. G

    Understanding Ampère's Law: How to Solve for Zero Current in a Closed Loop

    Homework Statement Would someone, please, show me that, if there is no current inside, that: \oint \vec B \cdot d\vec l=0 Please. Thanks. :smile: Homework Equations The Attempt at a Solution
  46. E

    Deriving B(r) from Ampere's law - For tomorrow (02/23)

    Hello again everyone Part of a problem I've been set is to show that the equation: B(r) = \frac{1}{2}\mu_0 (J x r) from Ampere's law: \nabla x B = \mu_0 J. The problem presents no... uh... problem thereafter, but I'm at a loss where to begin. I've been playing around with random...
  47. T

    Ampere's Law, must the current extend to infinity?

    Ampere's law states that, the closed integral of B over the loop enclosed it equals uI, where u = permeability of the material and I = current "passing" through the loop. I feel confused, because, should the current be extended to infinity? I mean, when we have an infinite wire of current...
  48. C

    Exploring Ampere's Law and Magnetic Fields at the Poles

    A north pole and south pole are separated by some distance (positioned vertically). Using the discrete version of Ampere's law: Take a path rectangle with one vertical side completely inside the magnetic field and the other vertical side completely outside the magnetic field. Where h =...
  49. Antepolleo

    Mutual Inductance and Ampere's law

    It's electromagnetics time again. I'm horribly stuck on a homework problem. It has to do with mutual inductance, and I know how the problem works conceptually, but I'm having a difficult time with the mathematics. The problem:A very long (read: infinite) wire is a distance d from the center of a...
  50. A

    Ampere's Law and current density

    The current density inside a long, solid, cylindrical wire of radius a = 10 cm is in the direction of the axis and varies linearly with the radial distance r cm from the axis according to J = J0 r / a with J0 =0.5 A/cm2 . Find the magnetic field in μT at r = 0.045 m Ok I know from amperes law...
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