1. Proportionalities R A aA a  ? 1. R- r 2. R+ r 3. R 2 / r 2 4. R 2 / r 5. R/ r 6. r /R a A r

2. Proportionalities R A aA a  ? 1.  R/ r 2. R/  r 3. R 2 / r 2 4.  R 2 / r 5. R/ r 6. r 2 /R 2 a r A

3. The same proportionalities work for arc-lengths R S R s r  r S s area at S R 2 area at s r 2 

4. + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + The electric field at the very CENTER of this spherical conductor E = ? 1. points out 2. points in 3. points up 4. points left 5. points right 6.points down 7.is zero

5. + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + What is the electric field at the very CENTER of this spherical conductor? E = 0!!

6. + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + The electric field at this off-CENTER point within the spherical conductor E = ? 1. points out 2. points in 3. points up 4. points left 5. points right 6.points down 7.is zero

7. + + + + + + + + + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Q=? q=?q=? Q/q=? R r

8. +++ ++++ Electrical Shielding In the presence of any nearby electric field the charge carriers within a conductor distribute themselves to effectively cancel the field in their own interior! - + NO FIELD! The interior is “shielded” from external magnetic fields

9. Gauss’ Law FLUX = E  A FLUX = “flow” number of lines entering or leaving a region (volume)

10. If more lines enter than leave denotes a concentration of negative charge within If more lines exit than enter denotes a concentration of positive charge within

12. A cube with edge, L, and surface area A on each face, is immersed in a uniform electric field E as shown. The flux through its bottom surface is 1.+ EA  EA 3.+ EL  EL 5. 0

13. A cube with edge, L, and surface area A on each face, is immersed in a uniform electric field E as shown. The flux through its top surface is 1.+ EA  EA 3.+ EL  EL 5. 0

14. A cube with edge, L, and surface area A on each face, is immersed in a uniform electric field E as shown. The flux through its front-facing surface is 1.+ EA  EA 3.+ EL  EL 5. 0

15. A cube with edge, L, and surface area A on each face, is immersed in a uniform electric field E as shown. The total flux through this cube is 1.+ 2EA  2EA 3.+ 6EL  4EL 5. 0

16. Flux = E  A Flux = 0 Flux = ?

17. Gaussian Surfaces

18. Heated filamentPositively charged can If the effective field is E =800,000 N/C over a gap length of 2.5 cm, what is the electron’s final velocity, v ? Electron Gun