- Coulomb's Law describes the electrostatic force of attraction or repulsion between two charged objects, and follows an inverse-square relationship with distance. The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. - The elementary charge, as determined by Millikan's oil drop experiment, is the lowest possible charge carried by a single electron or proton. Ordinary objects have charges that are integer multiples of this elementary charge. - Niels Bohr used the similarity between Coulomb's Law and Newton's Law of Gravitation to develop his atomic model of the hydrogen atom, with the electron orbiting the proton like planets orbiting the Sun.

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