- #1
Ngineer
- 64
- 1
Homework Statement
Very long wire carrying current I is surrounded by a brass ring of a triangular cross section. (figure attached)
Show that ψ =
Code:
μ° I h
------ (b - a ln ((a+b)/b)
2∏b
Homework Equations
A = (μ°I/2∏ * ln x) az (according to one of the solutions, where x is the distance between wire and surface)
ψ = ∫A.dl
The Attempt at a Solution
First attempt:
My first approach was to integrate the magnetic vector potential over the volume of the the ring, I defined the distance from the wire to the surface as:
d(x,z) = a + b(z/h) + x {0<= z<= h and 0<=x<=b(1 - z/h)
where
z is the rise in the z axis
x is the distance through the surface of the ring (i.e. distance penetrated through the surface)then I took ψ as a triple integral of
z from 0 to h
x from 0 to b(1-z/h)
θ from 0 to 2∏,
of (μ°I/2∏ * ln d(x,z)) az * dxdydθ
but I got a wrong answer
Second attempt
I took only the surface in consideration, i.e. removing all mention of θ. Still couldn't reach the original formula.
I spent almost 4 hours trying to figure this out. I looked up an online solution (out of genuine interest to know how the problem is solved, not academic dishonesty) and after a lengthy process they reach a different formula and claim that this is the solution!
This is really puzzling me because it looks rather simple, like I'm missing a basic formula or something.
Any help is greatly appreciated! Thanks!