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## Boundary Conditions

Knowing how electromagnetic fields change across boundaries is a common goal in undergraduate electricity and magnetism courses.

more explanation and activities for this sequence

### Activities

**Gauss's Law:**This small group activity has students use Gauss's law to find the electric field for a cylindrically or spherically symmetric charge density. Students are asked to make explicit symmetry arguments which make use of*Proof by Contradiction*.

**Ampere's Law:**Students use Ampere's law in this small group activity to find the magnetic field due to a radially dependent current density in an infinitely long cylindrical shell.

**Electric Field Continuity Across a Boundary:**Students use Ampere's and Gauss's laws to find the electric field just above and just below a plane which has a surface charge density $\sigma$. They find the continuity conditions for the electric field's parallel and perpendicular components across the planar boundary.

**Magnetic Field Continuity Across a Boundary:**Students use Ampere's and Gauss's laws to find the magnetic field just above and just below a plane which has a surface current, $\vec{K}$. The students find the continuity conditions for the magnetic field's parallel and perpendicular components across the planar boundary.

Add in homework and relationship to limits (going from the Gauss & Ampere activities to a planar boundary)