# What is Amperes law: Definition and 22 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. ### Cases when Ampere's circuital law fails to hold

Well, I guess that is pretty much my question.
2. ### 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!
3. ### Magnetic field of plane with thickness d with uniform surface current

I'm confused what's meant by a uniform surface current density since this plane has a thickness, It would need a current density distributed through its cross sections, I thought.Edit: I tried solving with proper LaTeX and all my steps, but it looked awful. For outside, I got B=µ_0jd/2. for...
4. ### Determining the B-field in center of current carrying loop

Homework Statement Determine the B-field inside the middle of a circular loop of current. Homework Equations Attempt at using Ampere's law: ##\oint \vec{B} \cdot d \vec{l} = \mu_0 i## The Attempt at a Solution ##\oint B \cdot R d \theta = \mu_0 i \Rightarrow BR(2 \pi) = \mu_0 i \Rightarrow B...
5. ### Magnetic field outside a conducting hollow cylinder

Homework Statement A current I flows along the surface of a hollow conducting cylinder. The radius of the cylinder section is r. By using Ampere's law, show that the magnetic field B outside the cylinder is B=\frac{\mu_0}{2 \pi} \frac{I}{r} Homework Equations Ampere's law...
6. ### Question on magnetic fields from wire

Homework Statement Homework Equations Biot-Savart's law and ampere's law expressing B = mu0 * I / (2 * pi * r) The Attempt at a Solution [/B] I know that for the first drawing, we have magnetic fields going into the page from both of the wires, and we have them being (infinitely) long, so...
7. ### Magnetic field in rectangular coil (not solenoid) Amperes law

Homework Statement I have a rectangular coil with length L and the cross-section's sides has length a and b (b>a). A wire is tightly wrapped around N times. Calculate the magnetic field inside the coil. Homework Equations The problem I have is that in class we were taught how to calculate...
8. ### Finding the magnetic field strength

Homework Statement There exists a current of 5A in the ay direction at x=2m,z=-2m where the ay is the unit vector in the y direction. Find the magnetic field strength at the origin. Homework Equations B = (μI/2πR) * r B = μH The Attempt at a Solution B = (μI/2πr) B= (4π*10^-7)(5)/2π(2) where...
9. ### The Relation between the integral and differential form of Amperes Law

The integral form of Ampere's law in vacuum is ∫B\cdotdl=μ_{0}I (a) Using the relation between I and J, obtain the differential form of Ampere's law. You may ignore any displacement current. (b)Define the displacement current density J_{d} in terms of the displacement field D and show...
10. ### Amperes Law conceptual confusion.

For amperes law it is stated that: ∫Bdl=μIenc My confusion is that B is that for example here now on Earth if I have a compass. It interacts with a the magnetic field of the Earth and points north. There is no I-enclosed yet there is still a magnetic field? Also another Amperes Law...
11. ### Magnetic field of an infinite current sheet : Amperes law

I was asked to find the magnetic field of an infinite current sheet due to amperes law. Is my attempt to the solution correct ? The final answer is correct, but l am doubtful of how l got there.
12. ### Why is the first term thrown away in the derivation of Ampere's Law?

Hi, I have some trouble understanding my book's derivation of Ampere's law. I have attached the derivation, and would like to ask the following. In equation 5.47 they throw away the first term because, ∇xJ=0. I don't understand why that is. Their argument is that J does not depend on the...
13. ### Amperes law: magnetic field inside an infinite slab containing a volume current.

Homework Statement an infinite slab is centered on the xy plane. the top of the slap is at z=a/2, the bottom of the slab is at z= -a/2. A volume current (J) is set up within the slab. find B everywhere J = k (1 - z^2/a^2) \hat{y} Homework Equations amperes law The Attempt at a...
14. ### Solving Amperes Law Problem - B=2.15T, Answer in Tm

Homework Statement A constant magnetic field points to the right. B= 2.15 T. Answer in Tm . Homework Equations ∫βDs=μI The Attempt at a Solution Just got introduced to these problems so not really sure how or what to integrate.3
15. ### Why Can't Ampere's Law Be Used for a Circular Arc Magnetic Field Calculation?

Homework Statement When I use Biot-Savart law to calculate the magnetic field at a distance from an arc, I get the well known B=\frac{i\mu_{0}\phi}{4 \pi R} Why can't I use Amperes law for this? I could imagine that the arc instead to be a complete loop of current. Then I could find...
16. ### Understanding Ampere's Law in Cylindrical Shell Configurations

If i have two cylindrical shells one inside the other , Like a pop can inside a larger pop can. And let's say they are infinitely long . And on the inner one i have a surface current and on the outer one i also have a surface current but in the opposite direction. The B field in between the...
17. ### Why Does Ampere's Law Use BL Instead of B(2L) for a Solenoid?

Lets take the infinite solenoid for example. Where we wrap wire around a pipe with current I. We make our amperian path a rectangle, half inside the solenoid half out. This site has the diagram I am talking about, a 1/4 way down the page...
18. ### Applying amperes law and faradays law to a solenoid and energy density

This isn't really a homework problem, I just need to know how to do a problem similar to this one for the final and I don't want to fail, so I posted it here. A solenoid with n turns per unit length, length l and radius a (l>>a) has a current I(t)==Io sin(wt) [w is omega], where I and w are...
19. ### Amperes law and electrodynamics and Gauss's law

It's evident that ampere's law is used to calculate the magnetic field produced by flowing charges. Can I use Gauss's Law to calculate the electric field produced by the flowing charges also? I ask this question because in the middle of a solid conductor, there is a flow of charge. However...
20. ### Modified Amperes law, maxwells equations

Using the following identity curl(curl(B))=Grad(Div(B)-Grad^2(B) with maxwells equations in differential form in the absences of sources show that magnetic field obeys the wave equation Grad^2(B)- (1/(C^2))(d^2(B)/dt^2) [b]2. The main probelm is I'm not sure what form of B i should use, i...
21. ### Deriving Magnetic Field Through Solenoid Using Amperes Law

[SOLVED] Amperes Law Homework Statement Deriving the magnetic field through a solenoid. Homework Equations dB = mu0/4pi x Idlsintheta/ r^2 where I = current dl= a tiny change in length dB = a tiny change in flux density sintheta is the angle to the normal r is the radius mu0 is the...
22. ### Need Help With Guass Laws and Amperes Law

Hi, I am really stuck with these problems, is it possible you guys can help me out, by guiding me along this problem, I wil write the entire thing out, but would appreciate it if you guys help me step by step so that I can understand it, since I am having a VERY hard time with these problems...