1. Electric Field Physics 102 Professor Lee Carkner Lecture 11

2. Force on Charges  F y = 8.99X10 9 (4)(2)/(4 2 ) =  F x = 8.99X10 9 (2)(5)/(3 2 ) =  F 2 = F x 2 + F y 2  F =  tan  = (F y /F x )   = arctan (F y /F x )   = 3 m 2 m q 2 = 5 C q 3 = 4 C q 1 =-2 C

3. Field Lines  E = k q/r 2   We would like to draw the field to give us a “map” of how the charge will effect other charges   Field lines indicate how a charge will move

4. Field Lines and the Field  What is the force on a small positive test charge?  Direction:   At any point the F vector is tangential to the field lines  Strength:   Density of lines proportional to field strength

5. Examples of Fields

6. Dipole  A common charge distribution is two charges equal in magnitude but opposite in sign   Electric field is strongest in the space between them 

7. Dipolar Field

8. How to Draw Field Lines   Lines point from positive to negative   More charge, more lines 

9. Today’s PAL  Draw below a point charge of +3q, and to the right, a point charge of –1q. Draw the electric field lines between them.  At a very large distance away, would a small positive test charge be attracted or repelled?  If q is one electron’s worth of charge, pick a point on a line connecting the charges and compute E there.

10. Van De Graaff Generator   The positively charged belt attracts the electrons in the dome making it positively charged  Belt moves electrons to a ground connection where they are dumped   Charge builds up until it is discharged through the air

11. Van De Graaff  Why does your hair stand up when you touch the Van De Graaff generator?   Why do you need to stand on the box? 

12. Van De Graaff Head E + ++ +

13. Conductors and Fields  What happens to a conductor in an electric field?   Like charges will want to get as far away from each other as possible 

14. Inside the Conductor  If we consider both positive and negative charge in an electric field,   A charge placed in the middle would feel an equal force from both sides and not move, thus,   For any point inside, the forces from all the charges cancel out 

15. Faraday Cage  If we make the conductor hollow we can sit inside it an be unaffected by external fields   Your car is a Faraday cage and is thus a good place to be in a thunderstorm 

16. Charge Distribution  How does charge distribute itself over a surface?   e.g., a sphere   No component parallel to surface, or else the charges would move   Excess charge there may spark into the air

17. Conducting Ring Charges Pushed To Surface No E Field Inside Field Lines Perpendicular to Surface

18. Electric Flux   If many field lines pass through a given area the forces there are strong   = EA  This is only true if the field in perpendicular to the area   = EA cos 

19. Finding Flux  The maximum flux occurs when the field is directly perpendicular to the surface:   The flux decreases as the angle increases until:   We also need to find the sign of the flux   If the field lines leave, the sign is positive  If the field lines enter, the sign is negative

20. Flux and Charge  To find the flux around a point charge we imagine a surface enclosing it  For a sphere of radius r around a charge q:   We can define the permittivity of free space:  0 = 1/(4  k) = 8.85 X 10 -12 C 2 /Nm 2   = q/  0

21. Gauss’s Law  What if we want to find the flux through an arbitrary surface?   The flux through any surface around a point charge is the same as through a sphere  = q/  0 (for any surface) 

22. Next Time  Read 17.1-17.6  Homework: Ch. 16, P 28, 31, 43, Ch. 17, P 2, 14