1. Coulomb’s Law and Electric Fields
Physics 102: Lecture 02
Coulomb’s Law and Electric Fields
Today we will …
get some practice using Coulomb’s Law
learn the concept of an Electric Field

2. Recall Coulomb’s Law
Magnitude of the force between charges q1 and q2 separated a distance r:
F = k q1q2/r2 k = 9x109 Nm2/C2
Force is
attractive if q1 and q2 have opposite sign
repulsive if q1 and q2 have same sign
Units:
q’s have units of Coulombs (C)
charge on proton is 1.6 x C
r has units of m
F has units of N
Calculate force on electron due to proton

3. Example
Three Charges
Calculate force on +2mC charge due to other two charges
Draw forces
Calculate force from +7mC charge
Calculate force from –7mC charge
Add (VECTORS!) F7
Q=+2.0mC
4 m
First get magnitude and direction for one, have students do the other, then say its math, then decompose using f_x = F x/r, f_y = f y/r Perhaps need to show this can be done with cosine and sine too.
Preflight: What is direction of force on third charge due to dipole
6 m
Q=+7.0mC
Q=-7.0 mC

5. Example
Three Charges
Calculate force on +2mC charge due to other two charges
Calculate force from +7mC charge
Calculate force from –7mC charge
Add (VECTORS!)
F+7
Q=+2.0mC
4 m
First get magnitude and direction for one, have students do the other, then say its math, then decompose using f_x = F x/r, f_y = f y/r Perhaps need to show this can be done with cosine and sine too.
Preflight: What is direction of force on third charge due to dipole
6 m
Q=+7.0mC
Q=-7.0 mC

6. Example
Three Charges
Calculate force on +2mC charge due to other two charges
Calculate force from +7mC charge
Calculate force from –7mC charge
Add (VECTORS!)
F+7
Q=+2.0mC
F = k q1q2/r2
5 m
4 m
F-7
First get magnitude and direction for one, have students do the other, then say its math, then decompose using f_x = F x/r, f_y = f y/r
Preflight: What is direction of force on third charge due to dipole
6 m
Q=+7.0mC
Q=-7.0 mC

7. Adding Vectors F+7+F-7 Example F+7 F-7 Q=+2.0mC 5 m 4 m 6 m Q=+7.0mC
First get magnitude and direction for one, have students do the other, then say its math, then decompose using f_x = F x/r, f_y = f y/r
Preflight: What is direction of force on third charge due to dipole

9. Adding Vectors F+7+F-7 Example y components cancel x components: F+7
Q=-7.0 mC
Q=+7.0mC
Q=+2.0mC
6 m
4 m
F+7
5 m
F-7
y components cancel
x components:
F = F+7,x + F-7,x
F+7,x = (3/5)F+7
F-7,x = (3/5)F-7
F = (3/5)(5+5)x10-3 N=6 x 10-3 N F
First get magnitude and direction for one, have students do the other, then say its math, then decompose using f_x = F x/r, f_y = f y/r
Preflight: What is direction of force on third charge due to dipole

10. Electric Field Example Charged particles create electric fields.
Direction is the same as for the force that a + charge would feel at that location.
Magnitude given by: E  F/q = kq/r2
Example +
r = 1x10-10 m
Qp=1.6x10-19 C E
If a tree falls in the forest, and no one is around to hear it, does it make a sound?
E = (9109)(1.610-19)/(10-10)2 N = 1.41011 N/C
(to the right)

11. Preflight 2.3 What is the direction of the electric field at point B?
Left
Right
Zero y A B x

13. ACT: E Field What is the direction of the electric field at point C?
Left
Right
Zero
Red is negative
Blue is positive y C x

14. Comparison: Electric Force vs. Electric Field
Electric Force (F) - the actual force felt by a charge at some location.
Electric Field (E) - found for a location only – tells what the electric force would be if a charge were located there:
F = Eq
Both are vectors, with magnitude and direction. Add x & y components. Direction determines sign.

17. Preflight 2.2 What is the direction of the electric field at point A?Up
Down
Left
Right
Zero
Red is negative
Blue is positive y A B x

18. ACT: E Field II
What is the direction of the electric field at point A, if the two positive charges have equal magnitude? Up
Down
Right
Left
Zero
Red is negative
Blue is positive y A B x

19. Electric Field of a Point Charge
0.81011 N/C
Example
321011 N/C
251011 N/C
2.91011 N/C + E
This is becoming a mess!!!

21. Electric Field Lines Closeness of lines shows field strength
- lines never cross
# lines at surface  Q
Arrow gives direction of E
- Start on +, end on -
After field lines up ask to compare efield at two points of equal distance

22. Preflight 2.5 Charge A is 1) positive 2) negative 3) unknownB X Y
Charge A is
1) positive 2) negative 3) unknown
Field lines start on positive charge, end on negative.

23. Preflight 2.6 Compare the ratio of charges QA/ QBX A B Y
Compare the ratio of charges QA/ QB
1) QA= 0.5QB ) QA= QB 3) QA= 2 QB
# lines proportional to Q

25. Preflight 2.8 The electric field is stronger when theA B X Y
The electric field is stronger when the
lines are located closer to one another.
The magnitude of the electric field at point X is greater than at point Y
1) True 2) False
Density of field lines gives E

26. ACT: E Field Lines B A
Compare the magnitude of the electric field at point A and B
1) EA>EB 2) EA=EB 3) EA<EB

27. E inside of conductor Conductor  electrons free to move
Electrons feels electric force - will move until they feel no more force (F=0)
F=Eq: if F=0 then E=0
E=0 inside a conductor (Always!)

29. Preflight 2.10 (1) Negative (2) Zero (3) PositiveB X Y
"Charge A" is actually a small, charged metal ball (a conductor). The magnitude of the electric field inside the ball is:
(1) Negative (2) Zero (3) Positive

30. Demo: electric field lines

31. Recap E Field has magnitude and direction: Electric Field Lines
EF/q
Calculate just like Coulomb’s law
Careful when adding vectors
Electric Field Lines
Density gives strength (# proportional to charge.)
Arrow gives direction (Start + end on -)
Conductors
Electrons free to move  E=0

32. To Do
Do your preflight by 6:00 AM _________.