Coulombs Law and Electric Fields

1
Coulombs Lawand Electric Fields
Physics 102 Lecture 02

• Today we will
• get some practice using Coulombs Law
• learn the concept of an Electric Field

2
Recall Coulombs 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
• qs have units of Coulombs (C)
• charge on proton is 1.6 x 10-19 C
• r has units of m
• F has units of N

5
3
Three Charges
Example

• Calculate force on 2mC charge due to other two
  charges
• Calculate force from 7mC charge
• Calculate force from 7mC charge
• Add (VECTORS!)

Q2.0mC
4 m
6 m
Q7.0mC
Q-7.0 mC
10
4
Three Charges
Example

• Calculate force on 2mC charge due to other two
  charges
• Calculate force from 7mC charge
• Calculate force from 7mC charge
• Add (VECTORS!)

Q2.0mC
4 m
6 m
Q7.0mC
Q-7.0 mC
10
5
Three Charges
Example

• Calculate force on 2mC charge due to other two
  charges
• Calculate force from 7mC charge
• Calculate force from 7mC charge
• Add (VECTORS!)

F7
Q2.0mC

• F k q1q2/r2

5 m
F-7
4 m
6 m
Q7.0mC
Q-7.0 mC
14
6
Three Charges
Example

• Calculate force on 2mC charge due to other two
  charges
• Calculate force from 7mC charge
• Calculate force from 7mC charge
• Add (VECTORS!)

F7
Q2.0mC

• F k q1q2/r2

5 m
F-7
4 m
6 m
Q7.0mC
Q-7.0 mC
14
7
Example
Adding Vectors F7F-7
8
Example
Adding Vectors F7F-7

• y components cancel
• x components

9
Example
Adding Vectors F7F-7

• y components cancel
• x components
• F F7,x F-7,x
• F7,x (3/5)F7
• F-7,x (3/5)F-7
• F (3/5)(55)x10-3 N6 x 10-3 N

You will have lots of opportunity to practice
this in homework and discussion
10
Gravitational Field An Analogy to the Electric
Field

• Force on m due to M
• F GMm/r2 GM/r2m
• Gravitational field due to M
• g GM/r2
• Force on m due to gravitational field
• F mg
• Identical to F GMm/r2

m
M
21
11
Gravitational Field An Analogy to the Electric
Field
q

• Force on q due to Q
• F kQq/r2 kQ/r2q
• Electric field due to Q
• E kQ/r2
• Force on q due to electric field
• F qE
• Identical to F kQq/r2

Q
21
12
Electric vs. Gravitational Fields

• Charges produces electric fields
• Just like masses produce gravitational fields
• Electric fields exert forces on charges
• Just like gravitational fields exert forces on
  masses
• Electric fields and gravitational fields are both
  vectors
• Gravitational field due to a mass always points
  towards that mass (e.g., toward the center of
  Earth)
• Electric field due to a charge Q points
• towards Q if Qlt0
• away from Q if Qgt0

13
Charged particles create electric fields.

• Direction points away from charge and toward
  charge.
• Magnitude given by E ? kq/r2
• Units N/C (Force/charge)

Example
E
E (9?109)(1.6?10-19)/(10-10)2 N/C 1.4?1011 N/C
(to the right)
21
14
Preflight 2.3

• What is the direction of the electric field at
  point B?
• Left
• Right
• Zero

72 16 9
it is closer to the negative charge, and the
field lines point toward negative charges .
B only has the charge from the negative which is
pushing away from itself .
electric fields of equal magnitudes but opposite
directions are present due to the positive and
negative charges .
Since charges have equal magnitude, and point B
is closer to the negative charge net electric
field is to the left
y
A
B
x
23
15
ACT E Field

• What is the direction of the electric field at
  point C?
• Left
• Right
• Zero

Red is negative Blue is positive
Away from positive charge (right)
Towards negative charge (right)
Net E field is to right.
y
C
x
25
16
ComparisonElectric 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.

26
17
E Field from 2 Charges
Example

• Calculate electric field at point A due to
  charges
• Calculate E from 7mC charge
• Calculate E from 7mC charge
• Add (VECTORS!)

A
Note this is similar to my earlier example.
4 m
You will have lots of opportunity to practice
this in homework and discussion
6 m
Q7.0mC
Q-7.0 mC
28
18
E Field from 2 Charges
Example

• Calculate electric field at point A due to
  charges
• Calculate E from 7mC charge
• Calculate E from 7mC charge
• Add vectors

E7

• E k q/r2

E-7
5 m
4 m
6 m
Q7.0mC
Q-7.0 mC
32
19
Adding Vectors E7E3
Example

• Decompose into x and y components.
• Add components.
• Note that y components cancel

E7
Etotal
5m
4 m
E-7
3m
6 m
Q7.0mC
Q-3.5 mC
35
20
Adding Vectors E7E3
Example

• Decompose into x and y components.
• Add components.
• Note that y components cancel

E7
Etotal
5m
4 m
E-7
3m
6 m
Q7.0mC
Q-3.5 mC
35
21
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
6 8 3 58 25
y
A
B
x
37
22
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
39
23
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 -

42
24
Rules for Electric Field Lines

• They start only on charges and end only on
  charges
• lines starting or stopping on a charge is
  proportional to the magnitude of the charge
• Tangent to field lines gives direction of field
  at that point
• Field lines can never cross
• Density of field lines is proportional to the
  strength of the field

25
Electric Field Lines
42
26
ACT/Preflight 2.5
Charge A is 1) positive 2) negative 3) unknown
Field lines start on positive charge, end on
negative.
93 4 3
44
27
ACT/Preflight 2.6
X
A
B
Y
Compare the ratio of charges QA/ QB 1) QA 0.5QB
2) QA QB 3) QA 2 QB
lines proportional to Q
12 9 63
45
28
ACT/Preflight 2.8
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
14 86
46
29
ACT E Field Lines
B
A
Compare the magnitude of the electric field at
point A and B 1) EAgtEB 2) EAEB 3) EAltEB
47
30
E inside of conductor

• Conductor ? electrons free to move
• Electrons feels electric force - will move until
  they feel no more force (F0)
• FEq if F0 then E0
• E0 inside a conductor (Always!)

48
31
ACT/Preflight 2.10
"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
9 74
18
50
32
Recap

• E Field has magnitude and direction
• E?F/q
• Calculate just like Coulombs 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 ? E0

33
To Do

• Read Sections 17.1-17.3
• Extra problems from book Ch 16
• Concepts 9-15
• Problems 11, 15, 23, 27, 29, 39
• Do your preflight by 600 AM Wednesday.

Have a great weekend. No classes Monday. See
you next Wednesday!