1. The document describes Gauss' law for calculating the electric field E due to a thin, infinitely large plane with a uniform surface charge density σ.
2. Due to the planar symmetry, the electric field E is uniform and directed perpendicular to the plane.
3. The magnitude of E is calculated using Gauss' law applied to a Gaussian surface consisting of boxes on both sides of the charged plane, giving E = σ / (2ε0)
2. Gauss’ Law for Planar Symmetry Question: Calculate E -field at arbitrary points at both sides of the plane Available: Thin flat plane, infinitely large, covered with surface charge density [C/m 2 ]
3.
4. Analysis and Symmetry (1) 1. Charge distribution: C/m 2 ] ; homogeneous. 3. Plane : infinitely large. 4. Front & Backside are equivalent. 2. Symmetry: Z-axis = symm. axis, perpendicular to plane. Z e z z X Y
5. Analysis and Symmetry (2) 8. Point charge in A : will not move // A due to symmetry 10. E : uniform field Z X Y e z z 5. Charge distribution: C/m 2 ] ; homogeneous. Plane A // charged plane: P P P P P P P P All points P equivalent 9. E : Z-component only !! 11. All A -planes equivalent
6. Analysis and Symmetry (3) 13. Conclusion from symmetry: uniform fields; opposite directions Z X Y e z z P P P P P P P P 12. Backside: similar situation
7.
8. Calculations sides do not contribute. only front and back lids contribute : charge enclosed: A 1 result: E 1 = E 2 = Z X Y e z z Gauss’ Law: back: A 2 choose Gauss-box: front: A 1 side walls
9. Conclusions field strength independent of distance to plane => homogeneous field the end Z for infinite plane:
![Gauss’ Law for Planar Symmetry Question: Calculate E -field at arbitrary points at both sides of the plane Available: Thin flat plane, infinitely large, covered with surface charge density [C/m 2 ]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)