1. Gauss’s Law AP Physics C

2. How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11 on p.696

3. Gauss’s Law Relates the electric field on a closed surface to the net charge within the system For static charges, Gauss’s Law and Coulomb’s Law are EQUIVALENT Gauss’s Law: The net number of lines leaving any surface enclosing the charges is proportional to the net charge enclosed by the surface

4. Electric Flux Φ The mathematical quantity that corresponds to the number of field lines crossing a surface For a surface perpendicular to the Electric Field, the flux is defined as the product of the magnitude of the field E and the area A: Φ = EA (units are Nm 2 /C)

5. The box may enclose a charge, by placing a test charge and observing F, we know E. It is only necessary to do this at the surface of the shape.

6. Pictures of outward (+) flux and inward (-) flux

7. Electric Flux Φ continued When the area is NOT perpendicular to E, then the following equation is used: Φ = EAcosθ = E n A Where E n is the component of E that is perpendicular or normal to the surface

8. Flux Flux, in this case Electric Flux, is the amount of (electric) field passing through a specified area. Think of water flowing in a pipe (flux comes from the Latin for “flow”)

10. Situations where the total flux equals zero

11. Ф = 0 through triangular prism below. E = 500 N/C 40 cm 50 cm 30 cm 40 cm

12. The E-field decreases at 1/r 2 while the area increases at r 2 and that increase and decrease cancel each other out and that is why the size of the surface enclosing Q does not matter.

13. Electric Flux Φ continued What if E varies over a surface? (see Fig 23-14 on p.697) If we take very small areas A that can be considered a plane, we can then sum the fluxes for each area using Calculus

14. Flux Symbol  Ф E Unit  Nm 2 /C Equation:

15. Quantitative Statement of Gauss’s Law P698 The net flux through any surface equals 4πk times the net charge inside the surface

16. Gauss’ Law

17. What we can conclude about Ф 1. Ф is proportional to q 2. Whether Ф is inward or outward depends on the q inside the surface 3. A q outside the surface offers zero Ф because Ф in = Ф out

18. Point Charge

19. Line of Charge

20. Sheet of Charge

21. Uniformly charge insulator at a varying r