# What is Ampere's law: Definition and 215 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. ### Magnitude of magnetic field at different points near a capacitor.

Here is a picture depicting the capacitor and the points of interest. I approached this problem by applying the Ampere-Maxwell law. For each point I used an circular Amperian loop that I denote by ##P##, enclosing a circular surface ##S##. Thus, for point ##b## we have...
2. ### I Are Maxwell's equations linearly dependent?

HI, consider the 4 Maxwell's equations in microscopic/vacuum formulation as for example described here Maxwell's equations (in the following one assumes charge density ##\rho## and current density ##J## as assigned -- i.e. they are not unknowns but are given as functions of space and time...
3. ### Magnetic field due to a long, straight wire

From Ampere's law, ##\displaystyle\oint\vec B\cdot d\vec l=\mu_0 I## where ##r## is the distance from the wire ##B\cdot 2\pi r=\mu_0 I## ##\displaystyle 91.4\times 2\pi\left(\frac{2}{100}\right)=4\pi\times 10^{-7} I## ##I=91.4\times 10^5\ A=9.14\ \rm{MA}## But the answer given in the...
4. ### I Does B=0 at points out of the plane containing and normal to a point current I?

Consider a point current I flowing at origin in the positive z direction. Biot Savart Law states that B field must move in an anticlockwise circle everywhere with the infinite line that the direction vector of the current, in this case the z axis, at the center. And its strength must be equal at...
5. ### I Ampere's Law For Static Magnetic Field

Hi there! Please refer to the picture below. I would like to understand the equation Curl(H) = J, where H is the magnetic field intensity and J is the current density. So, I inspect a simple problem. There is a wire carrying current I in the z-axis direction. a_r, a_phi, and a_z are the unit...
6. ### Length element in Ampere's law

Why is the length element (vector ds) perpendicular to the current? I though length element should be parallel to current. Would anybody be kind enough to help.
7. ### Ampere's Law for Cylindrical Conductor

I know that Ienl for the inner cylinder is just I and the current density for the outer tube is J1= -I/(pi(Ra^2-Rb^2). I assume that the current through the enclosed portion of the conducting tube (I1) is equal to J1(A1) where A1 is the area of the enclosed portion of the conducting tube. I...
8. ### Ampere's Law -- What is the meaning behind each part?

I believe it would be B(2pi b) but I'm not sure how exactly to explain why.
9. ### An iron cylinder inside a solenoid

From ##\oint_{\Gamma}\vec{H}\cdot d\vec{l}=\sum I## by Ampere's Law which gives ##H \Delta l=\Delta N\cdot i\Leftrightarrow H=n i## where ##n=## number of turns per unit length so ##i=\frac{H}{n}=\frac{10^3 A / m}{\frac{200}{0.2m}}=1 A##. Since ##\vec{H}=\frac{\vec{B}-\mu_0\vec{M}}{\mu_0}## we...
10. ### Why a transformer cannot use DC (Ampere's law)?

A direct current in the primary winding results in a constant magnetic field going through the center of the coil. If we have a magnetic core and a second winding, why doesn't the magnetic flux going through the core result in a current in the secondary coil, as well, according to Ampere's law?
11. ### How Is Ampere's Law Applied to Calculate Magnetic Fields?

(I accidentally missed my lesson and I don't know how to apply this question to the formula)
12. ### Ampere's Law for a toroid (finding relative permeability of iron)

Why is this equation: B(D - d)/mu + Bd = mu0 N I true? B = magnetic field in the hole of the toroid D = Average diameter of the toroid d = Diameter of hole of toroid mu = relative permeability of iron, or whatever the toroid is made of mu0 = 4pi x 10^-7 N = Number of turns on the toroid I =...
13. ### Solving Part e of the Electron Beam Problem

I am only asking about part e. If you are short on time, you can read through parts a - d, to get an idea of what is happening, and then attempt part e directly. I have solved parts a - d. If you would like to check your answers, the answer to part c is [rne^2 / 2e0] [ 1 - (v/c)^2], and the...
14. ### Engineering Need help about the magnetic field near an infinite current sheet

here is the question, don't mind about point (a) and (b) because i have solved them already...the main problem is the question on point (c) : so far, what i have done is : H = 2.7*0.1-(1.4*0.15+1.3*0.25) = -0.265 az A/m which is the wrong answer compared to the solution provided from the...
15. ### Ampere's law to find free current in a wire

∫ H.dl = ∫ j_f .dS = I_f ∇ x H = j_f I'm not sure how to actually solve this?
16. ### Using Ampere's Law for these two different integration paths

Homework Statement:: The magnetic field at every point on the path of integration Relevant Equations:: The scenarios/situations are shown in the attached photo. "Any conductors present that are not enclosed by a particular path may still contribute to the value of B field at every point, but...
17. ### Ampere's Law & Biot-Savart: Dealing with Infinity

How to lose surface integral in derivation of ampere law from biot-savart law if current goes to infinity? How does current that goes to infinity obey Helmholtz theorem for vector fields?
18. ### E&M: Field of a Wire with non-uniform current

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...
19. ### Determine the magnetic field inside and outside the cable using Ampere's law

My attempt: I realized after i had tried to solve the problem that the current must be constant in the cables. But no information about where the cables has radius a and b is given so how would I go about to find an expression for the current? Thanks in advance!
20. ### B field between the plates of a charging capacitor (Ampere's law)

A standard example consider a capacitor whose parallel plates have a circular shape, of radius R, so that the system has a cylindrical symmetry. The magnetic field at a given distance r from the common axis of the plates is calculated via Ampere's law: \oint_\gamma {\mathbf B} \cdot d{\mathbf...
21. ### Ampere's law -- application with two conducting loops

I am trying to get more confidence on the direction of current using Amperes law, the problem statement is Loop1: My first task was to assign the direction of current. If I wrap around the my right hand fingers in the direction of integration the thumb is pointing up hence Positive Y direction...
22. ### Ampere's Law Problem: B-Field from a Current Distribution

This is the problem, first time i am attempting the Ampere's law problem From the above question this is my attempt, the picture is ∫B.ds = μ*Ienc; ----> Ampere law , where Ienc is the current enclosed in the amperian loop. I assume the circle as the amperian loop, is it correct? Can i...
23. ### Magnetostatics and Ampere's law on a finite length wire

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...
24. ### Rewriting the Ampere's law in term of free currents only

This is not really the assignment of my homework ( my assignment require me to find the magnetic field inside a small air gap on a toroide magnet wrapped with N turns of a wire that carry a current I ) . I'm at some point in the solution where I kind of need to use the rewritten Ampere's law to...
25. ### Ampere's law in differential form

According to this image, in the attached files there is the demonstration of the ampere's law in differential form. Bur i have some difficulties in understanding some passages. Probably I'm not understanding how to consider those two magnetic vectors oriented and why have different name. in...

In Shadowitz's book The Electromagetic Field, Section 3-4, p. 129 to 134, there is a very interesting derivation of Ampere's Law. It is a general derivation with a circular source circuit S, and a circular test circuit T. The pages can be seen here, at least from where I post (USA)...
27. ### Why can't we use Ampere's Law?

We are asked to find the magnetic field at point P, all of the quantities in the figure are known values and the current density is uniform. One way to solve this problem is by modeling the sheet as a collection of infinitely long wires, with each wire contributing an amount of magnetic field dB...
28. ### Ampere's Law: Double Negative Line Integral Help

Hi all, I’m having some trouble finding a minus sign in a standard calculation I have been doing. I am trying to show that if there is no enclosed current around the example loop in the enclosed jpeg, the four piecewise paths add up to zero (for the line integral part of Amp’s law). For this...
29. ### Maxwell's Law of Induction - How Does it Work?

So, I was studying Maxwell's equations and I don't really understand the last one - Ampere's Law (with Maxwell's extra term added in). The bit I'm not able to understand is the term Maxwell added. How exactly does a changing electric field through a closed loop induce a magnetic field along that...
30. ### Applying Ampere's Law to a Transformer

Homework Statement I was wondering if and how we can apply Ampere's Law to a transformer? I am just thinking about the bog standard transformer with a core, primary coil, and secondary coil. 1) How do I deal with the current from both coils? 2) Do I need to think about the opposing magnetic...
31. ### Magnetic field inside a solenoid calculated with Ampere's law

I think the real magenetic field is sum of the magnetic fields calculated in each cross section of solenoid with various angle and same center axis when i apply Ampere's law. (Imagine the cross section contains a part of center line of the solenoid) Please let me know why we don't do like that. :)
32. ### Correct usage of Ampère's law for calculating B-field outside parallel wires?

Homework Statement The problem is basically about tow infinite parallel wires separated by a distance ##d## with equally strong but opposite currents. You have to calculate the B-field outside the wires (not the field in between them). Homework Equations Ampères law: ##\oint \mathbf B \cdot...
33. ### Ampere's law: what if we have a magnetic field but no current

If I have a magnetic field describing a closed path it means that this closed path is surrounding a current, right? But if I have no current, is it the displacement current ? I'm thinking of a magnetic dipole, its magnetic field describes closed paths from its north to south pole, so is there a...
34. ### Toroid with Air Gap magnetostatics problem

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...
35. ### Magnetic field in the gap of a tapered torus

Homework Statement Consider a toroidal electromagnet filled with a magnetic material of large permeability µ. The torus contains a small vacuum gap of length h. Over most of its length the torus has a circular cross section of radius R, but towards the gap the torus is tapered on both of its...
36. ### Ampere's Law with a coaxial cable

Homework Statement A portion of a long, cylindrical coaxial cable is shown in the accompanying figure. A current I flows down the center conductor, and this current is returned in the outer conductor. Determine the magnetic field in the regions (a) R ≤ r1, (b) r2 ≥ R ≥ r1, (c) r3 ≥ R ≥ r2, and...
37. ### Direction of the magnetic field around a solenoid

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...
38. ### Classical Book(s) with problems on classical electromagnetism

I started studying the book "A Student's Guide to Maxwell's Equations" by Daniel Fleisch some time back. It is an excellent book, giving a very good idea about the main laws of electromagnetism. I will soon finish the book. Now I need some book(s) which has problems on all the laws in classical...
39. ### Permittivity in Gauss' law and Ampere's law

In the derivation of the electric field inside a non conducting sphere, We still use the permittivity of free space even though we are in a medium. The same applies for ampere's law in a solid wire. http://physics.bu.edu/~duffy/semester2/c15_inside.html...
40. ### Biot-Savart's law and Ampere's Law -- are they the same?

Homework Statement Homework Equations is biot-savarat law and ampheres law equivalent? The Attempt at a Solution
41. ### Non symmetric case of Ampere's law

When we use Ampere's law, the most basic case that of an infinite current carrying wire is taken whose magnetic field is evaluated at a distance r from the wire. However there's nothing wrong in using the law for non symmetric scenarios. If this is the case how do you explain the B field at a...
42. ### Is Ampere's Law Affected by External Currents?

When we try to find magnetic field due to a set of current carrying wires in a region we draw an imaginary amperian loop and using ampere's law find the magnitude of the magnetic field. ##\oint \vec B \cdot d\vec l = \mu_{0}i_{enclosed}## The RHS involves only the enclosed current inside the...
43. ### Magnetostatics - Magnetic field of a nonuniform current slab

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...
44. ### Ampere's Law and Choosing a Loop for Integration

Homework Statement Homework Equations Amperes law The Attempt at a Solution This is a solution to an old exam and I am confused by the application of amperes law here. What is the general rule for drawing our "ampere'ian surface" when using amperes law? I thought we have to draw a...
45. ### Ampere's law to calculate the B field from a balanced three-phase system

I am a little confused when I try to use Ampere's law to calculate the B field from a balanced three-phase system. Consider the following, shown in the picture below: Lets say I want to calculate the value of B at a distance r (radius of my Amperian loop), the value of r is big enough so that...
46. ### Finding the direction of current given a varying magnetic....

Homework Statement Homework Equations μ0 In,e = ∫B⋅ds The Attempt at a Solution I really don't how to approach this question at all. Do you have to integrate counterclockwise around the loop every time? If the field was decreasing as y decreased, would you integrate CW or is it still CCW...
47. ### What is the value of I3 for the given line integral and values of I2 and B?

Homework Statement The value of the line integral around the closed path in the figure is 1.79×10−5 Tm . https://session.masteringphysics.com/problemAsset/1385538/4/32-22.jpg There is I2 and I3 inside the closed loop. I2 = 12 A What is I3? Homework Equations Amphere's Law: B = Uo I(enclosed)...
48. ### Magnetic field due to displacement current and Ampere's law

I have a doubt on this calculation of magnetic field in presence of displacement current. Consider a capacitor of radius ##R## and with plates at distance ##d## being charged: there is a displacement current in it. Suppose that I want to calculate the magnetic field ##B## at a distance ##r <...
49. ### The difference between Ampere's law & Biot-Savart Law

When considering the magnitude of the magnetic field at a certain point (##P##) away from an infinite/finite wire, I can't understand how an infinite wire would generate a stronger magnetic field (##B##) in contrast to a finite wire that has the same dimensions and current applied, at the same...
50. ### Voltages in an induced current

I've been messing around with ampere's and faraday's laws as we have recently been applying them in undergrad level physics. I'm confused as to how voltage fits in with these laws when used for a solenoid inducing a current in a material placed inside the solenoid. I know that the induced...