1. Physics 1202: Lecture 2 Today’s Agenda
Announcements:
Lectures posted on:
HW assignments, solutions etc.
Clicker: frequency code AA
Homework #1:
On Masterphysics this Friday
Homeworks posted on Masteringphysics
You need to register (included in cost of book)
Go to First Day of Class on syllabus for details
Course ID: cote90751
Problems: see Mairead Jacoby (Pearson)
Chemistry Cafe Friday between 10:00AM – 2:00PM
Labs start during the week of January 23. 1

2. Today’s Topic : Chap. 19 Review of Coulomb force
Define Electric Field in terms of force on "test charge"
Electric Field Lines
Electric Field of a point charge
Electric Field of plates
Shielding and charging by induction
Gauss’s law and applications

3. Recall Coulomb's Law Þ q2 r F12 q1 F21 q1q2 1 F12= r 4pe0 r2 1 4pe0
SI Units:
r in meters
q in Coulombs
F in Newtons Þ 1
4pe0
= k = N m2/C2
Charles Coulomb ( )

4. 19-4
Electric
Fields

5. Fields of all kinds... 77 73 72 75 82 71 77 84 68 80 64 73 83 82 88 55 66 88 80 75 88 90 83 92 91
These isolated Temperatures make up a Scalar Field
(you learn only the temperature at a place you choose)

6. Fields of all kinds...
It may be more interesting to know which way the wind is blowing … 77 73 72 75 82 71 77 84 68 80 64 73 83 57 56 55 66 88 80 75 88 90 83 92 91
That would require a VECTOR field.
(you learn how fast the wind is blowing, AND in what direction)

7. Electric Fields
The force, F, on any charge q0 due to some collection of charges is always proportional to q0:
Introducing the Electric Field:
a quantity, which is independent of that charge q0, and depends only upon its position relative to the collection of charges.
A FIELD is something that can be defined anywhere in space
it can be a scalar field (e.g., a Temperature Field)
it can be a vector field (as we have for the Electric Field)

9. Lecture 2, ACT 1 (a) (b) (c) Both charges Q1 and Q2 must be positive.x y E d
Two charges, Q1 and Q2 , fixed along the x-axis as shown, produce an electric field E at a point (x,y) = (0,d) which is directed along the negative y-axis.
Which of the following statements is true?
(a)
Both charges Q1 and Q2 must be positive.
(b)
Both charges Q1 and Q2 must be negative.
(c)
The charges Q1 and Q2 must have opposite signs.

10. How Can We Visualize the E Field?+ O
Vector Maps:
arrow length indicates vector magnitude
Graphs:
Ex, Ey, Ez as a function of (x, y, z) Er, Eq, EF as a function of (r, q, F)
+ chg x Ex

11. 19-5: Another Way to Visualize E ...
The Old Way: Vector Maps
A New Way: Electric Field Lines
Faraday
+ chg
- chg + O - + O
Lines leave positive charges and return to negative charges
Remember: test charge defining a field is positive
Number of lines leaving/entering charge = amount of charge
Tangent of line = direction of E
Density of lines = magnitude of E

12. Electric field lines
The charge on the right is twice the magnitude of the charge on the left (and opposite in sign), so there are twice as many field lines, and they point toward the charge rather than away from it.
positive: 8 lines → +q
negative: 16 lines → -2q

13. Various combinations of charges
Note that, while the lines are less dense where the field is weaker, the field is not necessarily zero where there are no lines. In fact, there is only one point within the figures below where the field is zero—can you find it?
dipole

14. Clicker question !
Two point charges, separated by 1.5 cm, have charge values of +2.0 and 4.0 C, respectively. Suppose we determine that 10 field lines radiate out from the C charge. If so, what might be inferred about the 4.0-C charge with respect to field lines?
a. 20 radiate out
b. 5 radiate out
c. 20 radiate in
d. 10 radiate in

15. 19.6 Conductor and shielding
Excess charges in conductors:
Free to move
Repel each other
End up on the surface
At equilibrium
No moving charges
E = 0 inside (otherwise test charge would move …)
Electric field perpendicular to surface
Otherwise, a force would move charges
Not at equilibrium !

16. 19.6 Electric field near Conductors
Conductor at equilibrium
E perpendicular to surface
E=0 inside
General shape
More charges at sharper curves
E larger there
Easier to accumulate charge in pointy objects
Lightning rod

17. 19.7 Electric Flux & Gauss’s Law
Measures E ⏊ to surface A
SI unit: N・m2 /C
Flux of a point charge +q
E = kq/r2 radially outward
Choosing a sphere centered on q
E is ⏊ to surface A

18. Gauss’s Law Defining permittivity of free space Gauss’s law
electric flux through a closed surface is proportional to the charge enclosed by the surface:

19. Gauss’s Law Useful to get electric field Charged plate
symmetry: E ⏊ to plate
uniformly charged: s = q/A
So E: constant magnitude
Useful to get electric field
By taking advantage of geometry

20. Electric Field Distibutions
Summary
Electric Field Distibutions
Dipole
~ 1 / R3
Point Charge
~ 1 / R2
Infinite
Line of Charge
~ 1 / R

21. Recap of today’s lecture
Define Electric Field in terms of force on "test charge"
Electric Field Lines
Examples
Charges in conductors
Electric Flux and Gauss’s Law
Homework #1 on Mastering Physics
From Chapter 19