2. The Electrostatic Force
• Charge of objects
• And separation distance
– Influence the force between them.

3. As q increases, F increases.

4. As D increases, F decreases.
Distance
Force

5. Coulomb’s Law
• Notice that d is squared!!!!!! This is
another example of an inverse-square
law.
1 2
2
c
elec
k q q
F
d
=
q charge
(Coulombs or C)
Distance (meter of m)
Electric Force
(Newtons or N)
kc (8.99 x 109
N-m2
/C2
)

7. Symmetries
• Recall Newton’s Law of Gravitation:
• And Coulomb’s Law:
• Notice the similarities??
1 2
2
c
elec
k q q
F
d
=
1 2
2grav
Gm m
F
d
=

8. Proportionality Constants
• Notice their relative size!!! 1020
difference!
1 2
2
c
elec
k q q
F
d
=
1 2
2grav
Gm m
F
d
=
G (6.67 x 10-11
N-m2
/kg2
) was a
proportionality constant
Newton’s Law of
Universal Gravitation
kc (8.99 x 109
N-m2
/C2
) is the
proportionality constant
Coulomb’s Law

9. Using Coulomb’s Law
• Why do they use such small numbers for ordinary
objects? Wouldn’t it make more sense to call
them 1 C instead??
• The answer lies in the famous “Oil Drop
Experiment.”

10. Using Coulomb’s Law
• So what sort of charges are we talking about?
q is 1-10 C
VERY LARGE
q is more like
10-6
or 10-9
C

11. The Elementary Charge
• http://webphysics.davidson.edu/applets/pqp_preview/contents/pqp_errata/c
d_errata_fixes/section4_5.html

12. The Elementary Charge
• Robert Millikan -1909
– electric charge is quantized.
• Quantized - things can only have certain
values, not just any value.
• Ex. Is it possible to own 2 ½ bicycles???
• Animation 1 (Quicktime)
• Animation 2 (Java)

13. The Elementary Charge
• Millikan demonstrated that all the oil
droplets had charges which were multiples
of each other!
• All the droplets carried some multiple of
what is called the Elementary Charge,
1.6 x 10-19
Coulombs.
• This is the charge of a single proton or
electron.
• Ordinary objects have charges like 10-9
C,
this is still about 10 billion excess
charges!!!

14. Using Coulomb’s Law
• Why is Coulomb’s Law called an “inverse-
square law?”
• Because of the d2
in the equation.
• Doubling the distance between objects cuts
the force by ¼ , just like Newton’s Universal
Law of Gravitation.
• Ex. Sound intensity, Spray paint, the
“Butter Gun”

16. The Inverse-Square Butter Gun

17. Bohr’s Model of Hydrogen
• You’ve seen the similarities between
Newon’s U.L.o.G. and Coulomb’s Law.
Niels Bohr used this similarity to create a
model of the Hydrogen atom.
• Just like the Earth orbiting the Sun, Bohr
pictured the electron orbiting the proton.
• Animation