Current and Resistance
Electric Charge and Coulomb`s
law
Lecture 20
Monday: 29 March 2004
Charge (q)
•
•
•
•
•
q is measured in coulombs (C)
q can be + or –
q is conserved
q is quantized
The elementary charge is:
• e = 1.6 ×10-19 C
Forces on Charges
• Unlike charges attract.
• Like charges repel.
Coulomb’s Law
1 q1q2
F
2
4 0 r
1
4 0
 8.99  10 N  m /C
9
2
 9.0  10 N  m /C
9
2
2
2
 0  8.85  10 C /N  m
12
2
2
Coulomb’s Law
1
q1q2
F
2
40 r
•Central Force (acts along the line connecting the two objects)
•“one over r squared force”
•Is mathematically identical to gravitational force.
m1m2
F G
r2
•But they are not the same force.
ELECTROSTATIC VS.
GRAVITATIONAL FORCE
• Electron: me = 9.11 × 10-31 kg
qe = – e = – 1.6 × 10-19 C
• Proton: mp = 1.67 × 10-27 kg
qp = e = 1.6 × 10-19 C
ELECTROSTATIC VS.
GRAVITATIONAL FORCE
•A proton and an electron are attracted to each
other by two forces:
mp me
Fgrav  G 2
r
2
q
q
1
1 e
p e
Felec 

2
2
40 r
40 r
ELECTROSTATIC VS.
GRAVITATIONAL FORCE
1
2
e
2
2
Felec
40 r
1
e


m p me 40 Gm p me
Fgrav
G 2
r
F
Felec
grav
39
 40
 2.3 10 or
 4.3 10
Felec
Fgrav
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?