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. Coulomb Law practice: Three Charges
Example
Coulomb Law practice: 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!)
F+7
Q=+2.0mC
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 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

4. Three Charges – Calculate forces
Example
Three Charges – Calculate forces
Calculate force on +2mC charge due to other two charges
Draw forces
Calculate force from +7mC charge
Calculate force from –7mC charge
Add (VECTORS!)
Calculate magnitudes
F+7
Q=+2.0mC
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 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. Three charges – Adding Vectors F+7+F-7
Example
Three charges – Adding Vectors F+7+F-7
Calculate components of vectors F+7 and F-7:
F+7
Q=+2.0mC
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

6. Three charges – Adding Vectors F+7+F-7
Example
Three charges – Adding Vectors F+7+F-7
Add like components of vectors F+7 and F-7:
F+7
Q=+2.0mC F
Final vector F has magnitude and direction
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
Double-check with drawing

7. 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)

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

9. Preflight 2.2 What is the direction of the electric field at point A?Up
Down
Left
Right
Zero y A B x

10. ACT: E Field What is the direction of the electric field at point C?
Left
Right
Zero y A C B x

11. E Field from 2 Charges Example
Calculate electric field at point A due to two unequal charges
Draw electric fields
Calculate E from +7mC charge
Calculate E from –3.5mC charge
Add (VECTORS!) A
Note: this is similar to (but a bit
harder than) my earlier example.
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
Preflight: What is direction of force on third charge due to dipole
6 m
Q = +7.0mC
Q = –3.5 mC

12. Comparison: Electric Force vs. Electric Field
Electric Force (F) – the actual force felt by a real charge at some location
Electric Field (E) – found for a location only (any location) – tells what the electric force would be if a charge were located there:
F = Eq
Both are vectors, with magnitude and direction.

13. Electric Field Map
Electric field defined at any location (we did three: A, B, C) y A C B x

14. Electric Field Lines This is becoming a mess!!!
Closeness of lines shows field strength (lines never cross)
Number of 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
This is becoming a mess!!!

15. Preflight 2.5 A B X Y
Charge A is
1) positive 2) negative 3) unknown

16. Preflight 2.6 Compare the ratio of charges QA/ QBX Y X A B Y
Compare the ratio of charges QA/ QB
1) QA= 0.5QB ) QA= QB 3) QA= 2 QB

17. Preflight 2.8 1) True 2) FalseB X Y
The magnitude of the electric field at point X is greater than at point Y
1) True 2) False

18. 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

19. 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!)

20. 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

21. Demo: E-field from dipoley A C B x

22. 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

23. To Do
Do your preflight by 6:00 AM Wednesday.