Ampere's law Definition and 211 Threads

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...

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} \...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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.

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...

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...

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...

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) =...

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...

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...

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...

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.

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...

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...

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...

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...

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...

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

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...

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

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

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

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...

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...

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

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.

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?

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...

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...

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...

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...

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...

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?

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...

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

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...

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...

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 =...

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...

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...

urgent help with ampere's law problem The problem reads as: Consider a hollow wire of inner radius a and outer radius b carrying a current I. Use Ampere's law to find the magnitude of the magnetic field B(r) as a function of distance r from the center of the wire. A) What is the current...

Hi I was wondering if you can help me. How is the concept of the displacement current used to resolve the ploblems with the application of Ampere's law. I know that the modified ampere's law is curl(B)=Mew(0)(jc+jd) I just know how the displacement current jd is used to solve the...