ece106: add ampere's law edge cases

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
+