diff --git a/crates/cross/src/step/mod.rs b/crates/cross/src/step/mod.rs
index 33c1996..694a2cf 100644
--- a/crates/cross/src/step/mod.rs
+++ b/crates/cross/src/step/mod.rs
@@ -213,6 +213,7 @@ impl<'a, R: Real, M: Material<R>> StepHContext<'a, R, M> {
 #[cfg(test)]
 mod test {
     use super::*;
+    use crate::compound::Optional;
     use crate::mat::Vacuum;
     use float_eq::assert_float_eq;
 
@@ -256,6 +257,41 @@ mod test {
         assert_vec_eq(new_h, Vec3::new(-2.0, 0.0, 2.0));
         assert_vec_eq(new_m, Vec3::zero());
     }
+    #[test]
+    fn step_h_understands_nabla_e() {
+        let mid = Vec3::new(4.0, 8.0, 12.0);
+        let ctx = StepHContext {
+            inv_feature_size: 1.0,
+            time_step: 1.0,
+            stim_h: Vec3::zero(),
+            mat: &Vacuum,
+            in_e: VolumeSamplePos {
+                mid,
+                xp1: Optional::some(mid + Vec3::new(1.0, 2.0, 3.0)),
+                yp1: Optional::some(mid + Vec3::new(4.0, 5.0, 6.0)),
+                zp1: Optional::some(mid + Vec3::new(7.0, 8.0, 9.0)),
+            },
+            in_h: Vec3::zero(),
+            in_m: Vec3::zero(),
+        };
+
+        //```tex
+        // $\nabla x E$:
+        //     $[ \Delta\!E_z/\Delta\!y - \Delta\!E_y/\Delta\!z$
+        //     $  \Delta\!E_x/\Delta\!z - \Delta\!E_z/\Delta\!x$
+        //     $  \Delta\!E_y/\Delta\!x - \Delta\!E_x/\Delta\!y ]$
+        // we take these values from `in_e`:
+        //    $[ 6.0 - 8.0 $
+        //    $  7.0 - 3.0$
+        //    $  2.0 - 4.0 ]$
+        // this gets negated, and then scaled by $\mu_0^{-1}$
+        //```
+
+        let (new_h, new_m) = ctx.step_h();
+        let b = -Vec3::new(-2.0, 4.0, -2.0);
+        assert_vec_eq(new_h, b * f32::mu0_inv());
+        assert_vec_eq(new_m, Vec3::zero());
+    }
     // TODO: backfill step_h tests
     // TODO: backfill step_e tests
 }