Homework Help: Linked and Bound Current

1. Nov 19, 2013

Philosophaie

1. The problem statement, all variables and given/known data
$magnitude(\vec{M})=NIS/c$ N is number of turns, I is current and S is the Area
$N/(unit length) =NS*cos\theta$ along a mathematical line

2. Relevant equations
Ampere Law $\int_C\vec{B}d\vec{l} = 4*\pi/c*I_{link}$

$I_{Bound} = c\int_C\vec{M}d\vec{l}$

$\int_C(\vec{B}-4\pi\vec{M})d\vec{l} = 4*\pi/c*I_{free}$

3. The attempt at a solution

$\vec{M} = NIS/c*cos\theta$

$I_{Bound} = c\int_C NIS/c*cos\theta d\vec{l}$
Help doing the Closed Loop integral with loop dl!

$\int_C(\vec{B}-4\pi\vec{M})d\vec{l} = 4*\pi/c*(I_{link}-I_{bound}) = 4*\pi/c*I_{free}$