diff --git a/docs/1b/ece106.md b/docs/1b/ece106.md index 15f5065..3bab104 100644 --- a/docs/1b/ece106.md +++ b/docs/1b/ece106.md @@ -614,6 +614,9 @@ where: $dl$ (along the loop) and $dS$ are related in direction with each other per the **right hand rule**. +!!! warning + Ampere's law is only true in when dealing with DC. + For each enclosed $I$, if its direction is: - the same as $\vec dS$, it is positive in the sum term @@ -622,3 +625,17 @@ For each enclosed $I$, if its direction is: 1. Use $dl$ to find $dS$ or vice versa 2. Determine $I_{enc}$ 3. Solve + +The angle of a cut to a surface does not affect any equations and can be treated identically. Any imaginary closed loop such that $\vec B$ **is constant over the loop and parallel to the loop** is usable with Ampere's law as $B$ can be reduced to a constant scalar. + +The geometries that work include: + +- Infinite cylinders with $J$ that may vary with $r$ but not $\phi$ +- Infinite sheets/slabs where $J$ may vary with $z$ but not $x,y$ +- Infinite selenoids +- Toroids (a selenoid bent into a donut shape) + +1. Create a cross-section perpendicular to the current and determine if symmetry of the loop can meet conditions for geometry +2. Choose $dl$ in the direction of $B$ (counterclockwise) +3. Determine $dS$ (out of the page) and apply Ampere's law +