Physics I
Class 19
Coulomb’s Law
19-1
Forces Known to Physics
(Review)
There are four fundamental forces known to physics:
 Gravitational Force (“yesterday’s news”)
 Electromagnetic Force (start today)
 Weak Nuclear Force
 Strong Nuclear Force
(All forces we observe are comprised of these fundamental
forces. Most forces observable in everyday experience are
electromagnetic on a microscopic level.)
19-2
A New Property of Matter Charge
 Charge comes in two types: positive and negative.
 NET charge can neither be created nor destroyed.
(Principle of Conservation of Charge)
 However, positive and negative charges can be separated or combined.
Neutral H
proton
electron
0 charge
+e charge
-e charge
 Charge is quantized – the smallest unit of charge (magnitude) in
normal experience is the charge of the electron or proton, “e”.
(All charges are integer multiples of this unit.)
 By arbitrary historical convention, the charge of an electron is negative
and the charge of a proton is positive.
19-3
Conservation of Charge
Charge is even conserved in nuclear reactions.
Here is what happens to a free neutron (outside a
nucleus) in about 12 minutes:
neutron
proton
electron
anti-neutrino
0 charge
+e charge
-e charge
0 charge
This is an example of the weak nuclear force (beta decay).
19-4
Coulomb - A Man, A Unit, A Law
Charles Coulomb, 1736-1806
Coulomb invented a delicate torsion balance with
which he was able to measure the forces between
charged and magnetic objects with sufficient
accuracy to verify a previous conjecture that the
mathematical formula for electromagnetic force
should resemble the formula for gravity.
The unit of charge is named after Coulomb, abbreviated C.
1.0 C = 6.24150975 × 10+18 e
1.0 e = 1.60217646 × 10–19 C
One Coulomb is a lot of protons!
19-5
Coulomb’s Law of
Electrostatic Force

1 q1 q 2
F
r̂ (Prof. B’s version.)
2
4  0 r
The meaning of each term:

F:
Electrostatic force on charge 1 from charge 2.
1
2
2
: Electrostatic force constant = 8.98755 × 10+9 N m /C
4  0
q1 : Value of charge 1, positive or negative.
q 2 : Value of charge 2, positive or negative.
r 2 : Center distance from point charge 1 to point charge 2.
r̂ :
Unit vector from charge 1 to charge 2.
19-6
Direction of Electrostatic Force
“Opposites Attract”
19-7
Properties of Electrostatic Force
Similarities with Gravity
 Every object with charge is attracted or repelled by every other
object with charge. (Opposites attract, same repel.)
 Electric force is a force at a distance (through occupied or empty
space).
 Electric force is a “central” force (center-to-center for point
charges).
 Electric force varies as the inverse square of the center distance.
 Electric force varies as the product of the charges.
19-8
Properties of Electrostatic Force
Differences with Gravity
 Electrostatic force is both attractive and repulsive,
depending on the signs of charge.
Gravity is always attractive.
 There is only one sign of mass and no way to “cancel
out” positive mass with negative mass.
 A charged object can attract an object with no net charge
by causing polarization (a Physics 2 topic).
 The electric force between a proton and an electron is far
larger than the gravitational force. (Next slide.)
19-9
Comparison of Gravity and
Electrostatic Force
r = distance between proton and electron (doesn’t matter)
M = mass of a proton = 1.67252 × 10–27 kg.
m = mass of an electron = 9.1091 × 10–31 kg.
2
2
G = gravitation constant = 6.673 × 10–11 N m /kg
e = charge of proton (+) or electron (–) = 1.60217646 × 10 –19 C
1
2
2
= electrostatic constant = 8.98755 × 10+9 N m /C
4  0
Considering only the ratio of the magnitudes:
Felec
Fgrav
1 e2
4  0 r 2
e2



M m 4  0 G M m
G 2
r
2.269 × 10+39
That number is dimensionless –
the same everywhere in the universe (as far as we know).
A deep mystery: Why is it so large?
19-10
Superposition of
Electrostatic Forces
+5.0 C
Y
1
X
resultant
N

Fon 1   
i2
+1.0 C
-3.0 C
1 q1 q i
r̂i (find and add X and Y components)
2
4   0 ri
19-11
How to Calculate a
Unit Direction Vector
From blue (x0,y0) to red (x,y):
1. Find
 the displacement in X,Y components.
d  ( x  x 0 ) î  ( y  y 0 ) ĵ  8 î  6 ĵ
2.
Find the length of this vector.
3.
Divide
 by the length to get a unit vector.

r  | d |  ( x  x 0 ) 2  ( y  y 0 ) 2  82  6 2  10


r̂  d  r  8î  6 ĵ  10  0.8î  0.6 ĵ
Y
6
0
X
0
8
19-12
Class #19
Take-Away Concepts
1.
Charges come in positive and negative.
2.
Opposites charges attract, like charges repel.
3.
Coulomb’s Law of Electrostatic Force

1 q1 q 2
F
r̂
2
4  0 r
4.
Similarities and differences with gravity.
5.
The principle of superposition.
N

Fon 1   
i2
1 q1 q i
r̂i
2
4   0 ri
19-13
Activity #19
Coulomb’s Law
(Another Pencil and Paper Activity)
Objective of the Activity:
1.
2.
3.
Think about Coulomb’s Law.
Consider the implications of the Coulomb’s Law formula.
Practice calculating electrostatic forces using superposition.
19-14