Register to reply

Ampere's Law on Current Carrying Loop

by JustStudying
Tags: ampere, ampere or biot, carrying, current, loop
Share this thread:
JustStudying
#1
Oct6-13, 06:24 AM
P: 27


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 however by the Biot-Savart Law we actually get

B = u*I / 2*r

anyone know why?
Phys.Org News Partner Physics news on Phys.org
Step lightly: All-optical transistor triggered by single photon promises advances in quantum applications
The unifying framework of symmetry reveals properties of a broad range of physical systems
What time is it in the universe?
phyzguy
#2
Oct6-13, 08:24 AM
P: 2,179
Ampere's law tells you that (line integral of B.dl along the loop) = μ0 * (flux of I through the loop). If you know from the geometry of the situation that B is constant along the loop, then calculating the line integral of B along the loop is easy. This is the case with a long straight wire. Here we draw a loop at a distance R from the wire. We know from symmetry that the value of B is everywhere constant along the loop, so the line integral of B along the loop is just 2*pi*R*B. In the case of a current carrying ring, no matter how you draw your Amperian loop, there is no way to draw it so that B is constant. So, while Ampere's law still holds, it is not very useful, since you don't know how to calculate the line integral. So you use the Biot-Savart law, which is more amenable to a general situation.


Register to reply

Related Discussions
Ampere's Law for current carrying wire Introductory Physics Homework 3
Ampere's Law (I think). Induced current from current carrying wire Introductory Physics Homework 12
Ampere's swimming rule about magnetic field around a current carrying conductor Classical Physics 1
Multiloop circuit, magnetic force on a current carrying wire, Ampere's Law Introductory Physics Homework 1
Torque on a current-carrying loop Introductory Physics Homework 2