The Electrostatic Force

• Charge of objects

• And separation distance – Influence the force between them.

As q increases, F increases.

As D increases, F decreases.

Distance

Force

Coulomb’s Law

• Notice that d is squared!!!!!! This is another example of an inverse-square law.

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celec

k q qF

d

q charge (Coulombs or C)

Distance (meter of m)

Electric Force(Newtons or N)

kc (8.99 x 109 N-m2/C2)

Symmetries• Recall Newton’s Law of Gravitation:

• And Coulomb’s Law:

• Notice the similarities??

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celec

k q qF

d

1 22grav

GmmF

d

Proportionality Constants

• Notice their relative size!!! 1020 difference!

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celec

k q qF

d

1 22grav

GmmF

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

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.”

Using Coulomb’s Law

• So what sort of charges are we talking about?

q is 1-10 CVERY LARGE

q is more like 10-6 or 10-9 C

The Elementary Charge

• http://webphysics.davidson.edu/applets/pqp_preview/contents/pqp_errata/cd_errata_fixes/section4_5.html

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)

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!!!

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”

The Inverse-Square Butter Gun

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