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. P

    Physics 2: Electromagnetic Theory (Amperè's Law, Biot-Savart, etc)

    Homework Statement First off: these are not homework problems technically, I'm doing these for my own benefit...they're not being graded or collected. Just trying to study for my final. Problem 1 A thin spherical, conducting metal shell has a radius of 15.0cm. A positive charge of 1.30µC...
  2. J

    Maxwell's modification to Ampere's law

    In my textbook, it uses a sack shape surface to explain why Ampere's law didn't work for a changing electric field between a capacitor. Why did they use this sack shape? Why not just use the same circle around the empty space between the capacitor, where its surface is normal to the electric...
  3. Y

    Ampere's Law: Current Enclosed in a Volume

    Homework Statement Ampere's Law uses the current enclosed in a: A) Loop B) Surface C) Volume Homework Equations The Attempt at a Solution I think the answer is C because I often see current in 3-dimensions, that is, it can be into or out of the page as well as up/down and...
  4. N

    Exploring the Limitations of Ampere's Law in Magnetic Field Calculations

    EDIT: I don't see this as a coursework question, even though I use a textbook example to set up my question. I feel that this is purely a conceptual question. If the staff disagrees, however, I am fine with this being moved to the homework forum. I have been very perplexed these past few...
  5. J

    Ampere's Law on Current Carrying Loop

    I haven't seen anyone derive the magnetic field density (B) using ampere's law, only using Biot-Savart Law any reason why? if we cut the loop and loop at one end (of the new cut) and treat it as if it was a current carrying wire, then by ampere's law we'd get: B = u*I / 2*pi*r but...
  6. L

    Why does Ampere's law only apply to enclosed currents?

    In my textbook it tells us ∫B ds = I μ (line integral and I = current enclosed) It also states that the current not enclosed does not affect the magnetic field along the line. I don't see a reason for other currents outside the loop not to affect the magnetic field thanks for any help
  7. C

    How Does Ampere's Law Apply to Complex Magnetic Field Configurations?

    Consider a hollow cylinder carrying a current I and a wire outside the cylinder carrying a current I'. Let's say the cylinder is symmetrical with even current distribution etc.. so the B field at any point (due to current in cylinder) within the cylinder is zero by Amperes Law. However, this...
  8. M

    Ampere's Law physical significance

    Hello, I am confused as to the physical significance of the dot product of B and ds. Why would we evaluate this scalar product. My textbook has it on here without any motivation for it. Also, why is the analogous gauss' law used with flux, yet magnetic flux doesn't use amperes law?
  9. R

    Ampere's Law: Cylindrical conducter with varying current

    Homework Statement The current density of a cylindrical conductor of radius R varies as J(r) = J0e−r/R (in the region from zero to R). Express the magnitude of the magnetic field in the regions r < R and r > R. (Use any variable or symbol stated above along with the following as necessary...
  10. R

    Ampere's Law: Determining magnetic fields of a shell conductor

    Homework Statement A current of constant density, J0, flows through a very long cylindrical conducting shell with inner radius a and outer radius b. What is the magnetic field in the regions r < a, a < r < b, and r > b? (Use any variable or symbol stated above along with the following as...
  11. J

    Quick question about Ampere's Law and how to use it?

    I just have a quick question about how to use Ampere's Law. It says that ∫B ds = u0(i_enc), which I suppose is easy enough to understand. But I'm having trouble reconciling it with the notion of, say, the magnetic field at the center of a loop of wire. The magnetic field at the center of a...
  12. B

    Cauchy's Integral Formula and Ampere's Law - Any Connection?

    I know how, by Amp\grave{e}re's Law for the loop integral of a magnetic field, $$\oint_C \textbf B \cdot d \textbf s = \mu_0 I$$ and this is zero when there is no current enclosed in the loop; there is a nonzero result when there is a current. With Cauchy's Integral Theorem, if a function is...
  13. D

    Ampere's Law and Magnetic Fields

    Homework Statement I have a coaxial cable with current density Jo in the center, with radius a, going in -z_hat direction. This generates a magnetic field. The outside of the cable, radius c, also carries a current density Jout going in the +z_hat direction. This generates its own magnetic...
  14. A

    Question about Ampere's law in vacuum and in matter

    Hi We can derive equation \nabla.D=\rho_f from equation \nabla.E=\rho/\epsilon_0. But what about Ampere's law? I tried to derive \nabla\times{H}=J_f+\partial{D}/\partial{t} from \nabla\times{B}=\mu_0J+\epsilon_0\mu_0\partial{E}/\partial{t} but I could not. This is strange because I thought...
  15. J

    Using Ampere's Law in finding H (magnetic field intensity)

    Homework Statement Let the regions 0 < z < 0.3 m and 0.7 < z < 1.0 m be conducting slabs carrying uniform current densities of 10 A/m^2 in opposite directions. Find H (the magnetic field intensity) and different z positions. Homework Equations Biot-Sarvot Law: H = ∫ (I dL X r)/ (4∏R2)...
  16. Z

    Ampere's Law and Magnetic Fields

    Homework Statement The figure shows a zero-resistance rod sliding to the right on two zero-resistance rails separated by the distance L = 0.53 m. The rails are connected by a 10.9-Ω resistor, and the entire system is in a uniform magnetic field with a magnitude of 0.750 T. (a) Find...
  17. L

    Electric Field using Ampere's law

    Consider the situation shown in Figure P24.1. An electric field of 300 V/m is confined to a circular area d = 11.0 cm in diameter and directed outward perpendicular to the plane of the figure. If the field is increasing at a rate of 22.0 V/m·s, what are direction and magnitude of the magnetic...
  18. J

    Understanding Ampere's Law: Exploring Complex Magnetic Fields and Amperian Loops

    I had a thought that I hope you could give me feedback on: Imagine a complex configuration that had a steady current, such that it's magnetic field was complex as well (I apologize for using 'complex' quite loosely here). If I were to apply Ampere's Law and form an Amperian loop that did not...
  19. B

    Ampere's Law for current carrying wire

    Homework Statement Use Ampere's Law to show that the equation for the magnetic field inside a current carrying wire is (1/2)μJr where J is the current density (assumed constant). Homework Equations ∫B*ds=μI The Attempt at a Solution ∫B*ds=μI B*ds=B(ds)cosθ I think θ...
  20. T

    Ampere's Law and Infinite Current Sheets

    Homework Statement Here is the question: http://dl.dropbox.com/u/64325990/HW%20Pictures/infinite%20current%20sheet.PNG Homework Equations ∫B(dot)dl = μoIenclThe Attempt at a Solution Here is my attempt: http://dl.dropbox.com/u/64325990/HW%20Pictures/Photo%202012-04-06%2010%2045%2008%20PM.jpg...
  21. G

    AP Physics: Understanding Ampere's Law for Wires and Solenoids

    I am studying AP Physics, and confused about the application of Ampere's Law. When we calculate the magnetic field due to a wire, we use: \mu_{0}I = \oint \vec{B}•\vec{dl} Does this only apply for straight wires that go off to infinity in both directions? We only focus on the current going...
  22. 1

    Ampere's law in a nonuniform conducting cylinder.

    Homework Statement A long, cylindrical conductor of radius R carries a current I. The current density, J, is not uniform and is given by the equation J = br, where b is a constant. Find an expression for the magnetic field magnitude B at distance r < R and at distance r > R. Homework...
  23. Q

    Ampere's Law with Maxwell's correction is equivelant to Ampere's Law?

    Is it true that Ampere's Law with Maxwell's correction is equivelant to Biot-Savart Law? Under what assumptions?
  24. E

    Ampere's law with quantum mechanics

    Ampere’s law – parallel electrical currents attract – has been known for a long time. How is that understood or explained in quantum mechanics?
  25. J

    Quick question about Ampere's Law and Lorentz force law

    Btw I am obtaining all these equations from chapter 5 of Griffiths text. Lorentz force law is: Fmag = ∫I(dI x B) Does this give the force on a current carrying wire due to an external magnetic field? (i.e. has nothing to do with own wires magnetic field) I think the answer is yes since the...
  26. C

    Ampere's Law in Classical Electrodynamics

    I do not know but I do not know if Ampers law is valid for short conductors passing through a loop. I did integrate and my integral was different from the expected I*U. The law seems to be valid only when long conductors pass through a loop but not short ones. Can anyone explain what am missing?
  27. G

    Solving Ampere's Law Trouble: My Mistake in Calculating B?

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  28. teroenza

    Ampere's Law vs Biot-Savart arouns a Square

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  29. S

    Magnetic field within cylinder using Ampere's Law

    Homework Statement Using Ampere's law, show that the magnetic field strength in a region within a cylinder, which has a constant current density j (flowing in the direction parallel to its axis), is equal to B = (mu-nought)*j*r/2 The Attempt at a Solution It doesn't say specifically, but...
  30. K

    How does Ampere's Law apply to a long thick slab on the z axis?

    Hey all- I'm a Junior in college, pretty much have Ampere's law down except there's always been one thing I don't quite understand and have just memorized. Say you have a long thick slab from -z to z on the z axis. J= J in the x direction. Find the B field in and out of the slab. My...
  31. M

    What is the role of surface currents in Ampere's Law with H fields?

    I'm using Griffiths Electrodynamics and I can't figure out something. For reference, this is on page 269 of the third edition. In the derivation for Ampere's law as it applies to the auxillary field H (i.e integral of H over a loop = free current passing through), there seems to be no word...
  32. F

    Magnetic induction of infinite conducting sheet using Ampere's Law

    Homework Statement http://i.imgur.com/j3uzQ.png" to screenshot of question Homework Equations The "Integral Form" the question refers to is the http://upload.wikimedia.org/math/0/3/1/0311484f33c932135c09ab12ca8d1a29.png" The Attempt at a Solution The hint hasn't really helped me...
  33. F

    Ampere's Law and Walter Lewin

    Homework Statement http://img18.imageshack.us/img18/8196/ampere.th.png Uploaded with ImageShack.usThe Attempt at a Solution I've watched Walter Lewin's vid http://www.youtube.com/watch?v=sxCZnb-EMtk&feature=relmfu like five times and he seemed pretty angry with the way books explain this...
  34. Y

    Ampere's Law and Laplace equations

    Homework Statement I need to write ampere's law (differential form) in the form of Laplace equations / Poisson equations and then solve them numerically using Matlab. Homework Equations Del x H = J The Attempt at a Solution pls see my attachment I need help from someone who is...
  35. H

    What is the motional emf of the loop at time t = 0.032 s?

    Homework Statement A conducting loop is made in the form of two squares of sides s1 = 3.8cm and s2 = 6 cm as shown. At time t = 0, the loop enters a region of length L = 18.6 cm that contains a uniform magnetic field B = 1.2 T, directed in the positive z-direction. The loop continues through...
  36. S

    Solving Ampere's Law Homework with Curve C

    Homework Statement In Ampere's Law, we consider an amperian loop (suppose a curve C), and any surface with boundary C can be chosen. 1.If the circulation of B is zero along the curve. Does this directly imply B=0 at points on the curve C? 2.Also in some cases there may be surfaces with...
  37. T

    Ampere's Law to find the magnitude of the magnetic field

    Homework Statement The wire in Figure 21-40 carries a current of 12 A. Suppose that a second long, straight wire is placed right next to this wire. The current in the second wire is 28 A. Use Ampère’s law to find the magnitude of the magnetic field at a distance of r = 0.72 m from the wires...
  38. D

    Problem in deriving Ampere's law

    Homework Statement I'm going through Jackson a bit, reading on Magnetostatics, and I came into a bump. I'm looking at \nabla\times B=\frac{1}{c}\nabla\times\nabla\times\int\frac{j(r')}{|r-r'|}d^3r' I expand that using 'BAC-CAB' rule and I get: \nabla\times...
  39. I

    How Does Ampere's Law Calculate Current in a Uniform Magnetic Field?

    Homework Statement Along a circular path the magnetic field is measured and is found to be uniform in magnitude and always tangent to the circular path. If the radius of the path is 0.03 m and B along the path is 1.4e-06 T, use Ampere's law to calculate the magnitude of the conventional...
  40. Q

    Using Ampere's law to find B just outside finite solenoid

    Homework Statement We have a solenoid of radius a, length L, with ends at z = +/- L/2. The problem is to use Ampere's law to show that the longitudinal magnetic induction just outside the coil is approximately B_z (\rho=a^+, z) \approx \left(\frac{2 \mu_0 N I a^2}{L^2} \right) \left(1+...
  41. G

    Ampere's Law with an open cylindrical shell

    Homework Statement A long, hollow conducting pipe of radius R and length L carries a uniform current I flowing around the pipe. Find expressions for the magnetic field (a) inside and (b) outside the pipe. Hint: What configuration does this pipe resemble? Homework Equations Ampere's Law...
  42. M

    Biot–Savart law and Ampere's law

    Hello, Just a quick question... in which cases do I use the Biot–Savart law and Ampere's law? ie. in what cases is it easier to calculate the magnetic field with the laws? Thanks
  43. A

    What are the differences between Biot-Savart Law and Ampere's Law?

    What is the difference between Biot- Savart Law and Ampere's Law ? both have same result in application . than what is the basic difference between them.
  44. M

    Deriving Biot Savart's law from Ampere's law

    Can anyone help me with this? My textbook (Young and Freedman's University Physics) says that Ampere's law can be extrapolated to give Biot Savart's law but I'm not sure how to go about it.
  45. J

    Ampere's Law: Calculating Magnetic Field Strength

    Homework Statement Homework Equations State Amperes Law. Show that the magnetic field at a distance R from a very long straight wire carrying a current I has magnitude μ I / (2 pi R) The Attempt at a Solution I really don't know :(
  46. Q

    Ampere's law for a closed ring bar magnet

    Homework Statement A long bar magnet is bent into the form of a closed ring. If the intensity of magnetisation is M, and ignoring any end effects due to the join, find the magnetic field H and the induction B: (a) Inside the material of the magnet (b) just outside Homework Equations...
  47. H

    Equivilence between Biot-Savart's Law and Ampere's Law

    I am considering the equivilence between Biot-Savart's Law and Ampere's Law for a current loop. The form of the magnetic field from a current element in the Biot-Savart law becomes dB = \muoI dL sin\theta/4\pir2 which in this case simplifies greatly because the angle =90 ° for all points...
  48. M

    Why do we assume cylindrical symmetry in Ampere's Law?

    When you're trying to find the magnetic field inside a current carrying wire using Ampere's Law, how do you know that the magnetic field inside also displays cylindrical symmetry?
  49. M

    Understanding Ampere's Law: Clarifying the Role of External Currents

    I can't seem to understand why a current outside of a loop doesn't contribute in Ampere's Law? Any clarification would be appreciated.
  50. K

    Ampere's Law and straight wires

    The figure below shows two long, straight wires in the xy plane and parallel to the x axis. One wire is at y = −6.0 cm and the other wire is at y = +6.0 cm. The current in each wire is 19 A. If the currents are both in the −x direction, find the magnetic field at the following points on the y...
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