Electric flux, Gauss’s law

1. Electric flux, Gauss’s law Carl Friedrich Gauss Physics 122 Lecture IV

2. Concepts • Primary concepts: • Electric flux Lecture IV

3. Laws • Gauss’s law Lecture IV

4. Definition of electric flux • Flux means flow • Nothing is actually flowing • Other than that thinking of flow really helps to understand the flux Lecture IV

5. Electric flux • If electric field is rain – electric flux is the amount of water in a bucket accumulated per unit of time: • Only component of the field perpendicular to the area A contributes to the flux Lecture IV

6. Electric flux • Alternatively we can define a vector A, which equals to the area A and is directed perpendicularly to the area Flux is proportional to the number of field lines going through the surface Lecture IV

7. Compare fluxes Which flux is larger? 1). F1>F2 2). F1<F2 3).F1=F2 2 1 Lecture IV

8. Compare fluxes Which flux is larger? 1). F1>F2 2). F1<F2 3).F1=F2 2 1 Lecture IV

9. Compare fluxes Which flux is larger? 1). F1>F2 2). F1<F2 3).F1=F2 1 2 Lecture IV

10. Compare fluxes Which flux is larger? 1). F1>F2 2). F1<F2 3).F1=F2 1 2 Lecture IV

11. Compare fluxes Which flux is larger? 1). F1>F2 2). F1<F2 3).F1=F2 1 2 Lecture IV

12. Compare fluxes Which flux is larger? 1). F1>F2 2). F1<F2 3).F1=F2 2 1 Lecture IV

13. Non-uniform field, irregular surface • Closed surface • Influx <0 • Outflux>0 Don’t worry, we’ll only deal with simple surfaces Complex surfaces can be handled using numeric integration by a computer. Lecture IV

14. Why do we need flux? • Gauss’s law: Lecture IV

15. Gauss Coulomb • Calculate E of point like (+) charge Q • Consider sphere radius r centered at the charge • Spherical symmetry: E is the same everywhere on the sphere, perpendicular to the sphere Lecture IV

16. Sinks and sources • What goes in – goes out • unless • there is a source (positive charge) • or a sink (negative charge) + - Lecture IV

17. What’s the flux? • F1=? F2=? Lecture IV

18. Respect the symmetry • Find electric field for the following configurations: • Uniformly charged sphere. Charge Q, radius R. • Long uniform line of charge. Charge per unit length l. • Infinite plane of charge. Charge per unit of area s Lecture IV

19. Field near conductor • Infinite plane of charge. Charge per unit of area s • Field inside conductor is zero, outside perpendicular to the surface. Lecture IV

20. Respect the symmetry • Find electric field for the following configurations: • Uniformly charged sphere. Charge Q, radius R. • Long uniform line of charge. Charge per unit length l. • Infinite plane of charge. Charge per unit of area s Lecture IV

21. Two parallel plates • Infinite plates • One positive, one negative, • Same charge density s + - Lecture IV