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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 (Estimated time: 60 minutes): 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 (Estimated time: 45 minutes): 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 (Estimated time: 10-20 minutes): 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 (Estimated time: 10-20 minutes): 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)

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