Electricity and Magnetism
Coulomb’s Law
Lana Sheridan
De Anza College
Sept 23, 2015
Last time
• introduced charge
• conductors
• insulators
• induced charge
.
Warm Up: Worksheet
.
3. Do both balloons A and B have a charge?
entry by
n entering the
rds each other
ne another
rge
opposite type
(A) yesor
r charged
(B) no, neither is charged
(C) at least 1 is charged.
ons being
.
Warm Up: Worksheet
.
3. Do both balloons A and B have a charge?
entry by
n entering the
rds each other
ne another
rge
opposite type
(A) yesor
r charged
(B) no, neither is charged
(C) at least 1 is charged.
ons being
←
charged or
Warm Up: Worksheet
5. Does this happen?
g straight
at _____.
re identical
other and both
(A) yes
(B) no
charged or
Warm Up: Worksheet
5. Does this happen?
g straight
at _____.
re identical
other and both
(A) yes
(B) no
← consider Newton’s 3rd law
Overview
• Force from a point charge
• Quantization of charge
• Charge conservation
Electrostatic Forces
Charged objects interact via the electrostatic force.
The force that one charge exerts on another can be attractive or
repulsive, depending on the signs of the charges.
• Charges with the same electrical sign repel each other.
• Charges with opposite electrical signs attract each other.
Charge is written with the symbol q or Q.
Charge is Quantized
quantization
A physical quantity is said to be quantized if if can only take
discrete values.
Originally, charge was thought to be a continuous fluid, but it is
not.
Charge is Quantized
quantization
A physical quantity is said to be quantized if if can only take
discrete values.
Originally, charge was thought to be a continuous fluid, but it is
not.
Just like water has a smallest unit, the H2 O molecule, charge has a
smallest unit, written e, the elementary charge.
e = 1.602 × 10−19 C
Any charge must be
q = ne ,
n∈Z
Question
Initially, sphere A has a charge of −50e and sphere B has a charge
of 20e. The spheres are made of conducting material and are
identical in size. If the spheres then touch, what is the resulting
charge on sphere A?
(A) −50e
(B) −30e
(C) −15e
(D) 20e
Question
Initially, sphere A has a charge of −50e and sphere B has a charge
of 20e. The spheres are made of conducting material and are
identical in size. If the spheres then touch, what is the resulting
charge on sphere A?
(A) −50e
(B) −30e
(C) −15e
(D) 20e
←
Conservation of Charge
Charge can move from one body to another but the net charge of
an isolated system never changes.
This is called charge conservation.
Conservation of Charge
Charge can move from one body to another but the net charge of
an isolated system never changes.
This is called charge conservation.
What other quantities are conserved?
Conservation of Charge
One interesting phenomenon that shows the conservation of charge
is pair production.
A gamma ray (very high energy photon) converts into an electron
and a positron (anti-electron):
γ → e− + e+
New mass is created out of light, but charge is still conserved!
Electrostatic Forces
For a pair of point-particles with charges q1 and q2 , the magnitude
of the force on each particle is given by Coulomb’s Law:
F1,2 =
ke q1 q2
r2
ke is the electrostatic constant and r is the distance between the
two charged particles.
ke =
1
4π0
= 8.99 × 109 N m2 /C2
How Coulomb’s Law
Torsion
Balance
694 was found:
Chapter 23
Electric Fields
Suspension
head
23.3 Coulomb’s L
Charles Coulomb measured
objects using the torsion ba
ciple of the torsion balance
to measure the density of t
spheres replaced by charge
and B in Figure 23.5 causes
resulting motion causes the
of the twisted fiber is prop
measurement of this angle
attraction or repulsion. On
between them is very large
gravitational force can be n
From Coulomb’s experi
B
force (sometimes called th
A
ticles. We use the term po
The electrical behavior of e
them as point charges. Fro
tude of the electric force (
23.5
Coulomb’s
balance, and
1
Figure from Serway &Figure
Jewett,
Physics
for Scientists
Engineers, 9th ed.
Fiber
Electrostatic Forces: Coulomb’s Law
F1,2 =
ke q1 q2
r2
Remember however, forces are vectors. The vector version of the
law is:
F1→2 =
ke q1 q2
r̂1→2
r2
where F1→2 is the force that particle 1 exerts on particle 2, and
r̂1→2 is a unit vector pointing from particle 1 to particle 2.
Coulomb’s Law
Coulomb’s Law:
F1→2 =
Does this look a bit familiar?
k q1 q2
r̂1→2
r2
Coulomb’s Law
Coulomb’s Law:
F1→2 =
k q1 q2
r̂1→2
r2
Does this look a bit familiar?
Similar to this?
F1→2 = −
G m 1 m2
r̂1→2
r2
Coulomb’s Law
F1→2 =
tric Fields
When the charges are of the
same sign, the force is repulsive.
S
When the charges are of opposite
signs, the force is attractive.
"
q2
S
r
!
q1
k q1 q2
r̂1→2
r2
!
q2
F12
S
F12
S
rˆ12
!
q1
F21
F21
a
b
same sign1as
in Figure
23.6a,&
the
product
q 1q 2 for
is positive
and
electric 9th
force
Figure
from Serway
Jewett,
Physics
Scientists
andthe
Engineers,
ed.on one
Electrostatic Constant
The electrostatic constant is:
k=
1
= 8.99 × 109 N m2 C−2
4π0
0 is called the permittivity constant or the electrical
permittivity of free space.
0 = 8.85 × 10−12 C2 N−1 m−2
Summary
• Force from a point charge
Homework
• Collected homework 1, posted online, due on Monday, Oct 5.
Serway & Jewett:
• Read Ch 23
• Ch 23, onward from page 716. Conceptual Qs: 5; Section Qs:
1, 3, 11, 13, 16, 17