Physics 212
Electric Force
D
Dependence
d
on Amount
A
t off Ch
Charge
Dependence on Distance
Magnitude of the Coulomb Force
Direction of the Coulomb Force
Coulomb Force as a Vector
Multiple Particles and Forces
1
Physics 212
Electric Force
The amount of electric force between two particles
depends on the amount of charge each has.
q
-q
q = 1 µC
q
q
q = 2 µC
q = 3 µC
-q
-q
2
1
Physics 212
Electric Force
The amount of electric force between two particles
depends on the distance between them.
q
-q
q
3
-q
This dependence is inverse and square.
Physics 212
Electric Force
What did Charles-Augustin Coulomb discover?
The force between two charges is directly proportional to the
magnitude
g
of each charge.
g
The force between two charges is inversely proportional to the
square of the distance between them.
The constant of proportionality has the value
k=
1
4πε 0
= 8.99 × 109 Nm2 /C2
Like charges repel along the line between them and unlike
charges attract along the same line.
4
2
Physics 212
Electric Force
In equation form, we have the magnitude of the
Coulomb force…
q1q2
F =k 2
r
q2
r
q1
5
It has the same magnitude for both particles !!!!
Physics 212
Electric Force
The direction of the Coulomb force is…
away from the other particle if they are alike
q2
F̂2,1 = r̂2,1
F̂ˆ1, 2 = r̂1, 2
q1
and toward each other if they are opposite.
F̂2,1 = r̂2,1
q1
-q2
F̂1, 2 = r̂1, 2
6
3
Physics 212
Electric Force
In general, Coulomb’s Law can be written…
→
F1, 2
q1q2 ∧
= k 2 r1, 2
r1, 2
and
d should
h ld be
b added
dd d along
l
with
ith Normal
N
l Force,
F
Tension, Gravity, Friction and Elastic Force in a freebody diagram.
7
Physics 212
Electric Force
Note that Coulomb’s Law works even for a sphere…
→
F1, 2
q1q2 ∧
= k 2 r1, 2
r1, 2
as long as you remember that r is the distance
between the center’s of the sphere.
8
4
Physics 212
Electric Force
An example of using Coulomb’s Law…
Q. A what radius does the electron orbit in a hydrogen atom?
What force act on the electron?
Gravity
Electric
What is its magnitude?
e2
F =k 2
r
What does Newton’s Second Law tell us?
9
e2
v2
F = k 2 = ma = m
r
r
k e2
r=
m v2
Physics 212
Electric Force
D
Dependence
d
on Amount
A
t off Ch
Charge
Dependence on Distance
Magnitude of the Coulomb Force
Direction of the Coulomb Force
Coulomb Force as a Vector
Multiple Particles and Forces
10
5