1. Electricity Electric Flux and Gauss’s Law 1 Electric Flux Gauss’s Law Electric Field of Spheres Other Gaussian Surfaces Point Charges and Spheres

2. Electricity Electric Flux and Gauss’s Law 2 Flux is defined as the amount of an electric field passing perpendicularly through a surface. For an electric field passing perpendicular to a plane, it is… A E

3. Electricity Electric Flux and Gauss’s Law 3 What if the electric field is not perpendicular? A A θ A E E

4. Electricity Electric Flux and Gauss’s Law 4 What if the surface is a closed surface? q E

5. Electricity Electric Flux and Gauss’s Law 5 In general, Gauss’ Law states that for any imaginary closed surface Gauss’ law is always true but not always useful. Q inside is the charge inside the imaginary surface.  is the total flux through this surface. We use Gauss’ law to calculate E. Gauss’ law is easy to use if the electric field vector is perpendicular to the chosen surface.)

6. Electricity Electric Flux and Gauss’s Law 6 Rules for Conductors All excess charge within a conductor moves to its surface. The electric field inside the material that makes up a conductor is zero. Electric fields just outside the surface of a conductor are perpendicular to its surface. Gauss’s Law is usually the best way to find the electric field of a conductor.

7. Electricity Electric Flux and Gauss’s Law 7 Q E r The electric flux from Gauss’ Law The electric field Outside any Sphere A sphere with total charge Q An imaginary Gaussian surface

8. Electricity Electric Flux and Gauss’s Law 8 Q E r The electric flux Gauss’ Law The electric field Outside any Spherical Shell

9. Electricity Electric Flux and Gauss’s Law 9 Q E r The electric flux Gauss’ Law The electric field Inside any Spherical Shell R

10. Electricity Electric Flux and Gauss’s Law 10 For a cylinder or a plane, the principal is the same but the surface used changes Note that the end faces must be included unless the cylinder is infinitely long. EnEn EnEn

11. Electricity Electric Flux and Gauss’s Law 11 q Q E r The electric flux Gauss’ Law The electric field Outside a Conductor with a Point Charge Inside

12. Electricity Electric Flux and Gauss’s Law 12 q Q E r The electric flux Gauss’ Law The electric field Inside a Conductor with a Point Charge Inside R

13. Electricity Electric Flux and Gauss’s Law 13 Q q E r The electric flux Gauss’ Law The electric field Outside a Conductor with a Point Charge Outside

14. Electricity Electric Flux and Gauss’s Law 14 Q q E r The electric flux Gauss’ Law The electric field Inside a Conductor with a Point Charge Outside (it works as a shield and lets no electric field inside its walls) R