Electric flux, Gauss’s law

1. Electric flux, Gauss’s law Carl Friedrich Gauss Physics 114 Lecture III

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

3. Laws • Gauss’s law Lecture III

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 III

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 III

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 III

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

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

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

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

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

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

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 III

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

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 III

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

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

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 III

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 III

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