PHY10004
Week 1a Essentials
Chapter 20
• electric charge
• electric force
• Coulomb’s Law
Electric charge (or simply “charge”)
• electric charge is a fundamental property of matter
protons and electrons have charge (and mass, spin, etc.)
One way we are know it exists is by
the force between charged objects
Two types of charge
+ positive
− negative
same signs of charge repel each other
opposite signs of charge attract each other
Electric charge is quantised
• objects have an integer multiple of the elementary charge
symbol for charge: q or Q
𝑞𝑒 , 𝑒
SI unit of charge: coulomb, C
qe = 1.60 x 10-19 C
protons and electrons have the same magnitude of charge,
with opposite signs
qproton = +1.60 x 10-19 C
qelecton = −1.60 x 10-19 C
Electric charge is conserved
• total charge of a closed system remains constant
no net charge can be created or destroyed
Example: a gamma ray can be
converted to an electron and a positron
𝐸 = 𝑚𝑐 2
gamma ray → electron + positron
zero
+qe
−qe
charge
zero
“pair production”
𝛾
𝑒−
𝑒+
Electric force – Coulomb’s Law
• understanding the force between two point charges
The force between two charges depends on
the magnitude and sign of each charge, and
the distance between them
𝑘𝑞1 𝑞2
𝐹=
𝑟2
q1
q2
r
Coulomb’s Law
k = 9.0 x 109 N m2/C2
force direction is along the
line joining the two charges
same signs repel
opposite signs attract
+
+
−
−
+
−
Electric force – superposition
• more than just two point charges
The net electric force on a charge is the vector sum of all the
individual electric forces acting on it
𝑘𝑞1 𝑞2
𝐹21 = 2
𝑟12
𝐹Ԧ21
𝑘𝑞1 𝑞3
𝐹31 = 2
𝑟13
𝐹Ԧ1,net = 𝐹Ԧ21 + 𝐹Ԧ31
𝐹Ԧ21
𝐹Ԧ31
𝐹Ԧ1,net
q1
q2
+
+
𝐹Ԧ1,net
𝐹Ԧ31
−
q3
Electric charge and force
• Now work through the following:
Wolfson Chapter 20
sections 20.1 and 20.2
all examples in these sections
PhysCasts on Canvas (Electric Charge, Force and Field)
Four Charges on a Square
Levitating an Electron
PHY10004
Week 1b Essentials
Chapter 20 (cont.)
• electric field
Electric field
• A useful way to describe the electric force
a point charge can exert a force
on any other charge near it
+
there is a “region of influence”
around the charge; a “force field”
use an arbitrary “test” charge to
map the “force field” around the
point charge
by convention the “test” charge
is a positive charge
+
Electric field
• Define a field 𝐸 as the force per unit charge
electric field is defined in terms of the
electric force on a (positive) test charge
𝐹Ԧ
𝐸=
𝑞
+
[units: N/C]
when the electric field is known,
we can easily calculate the force
on ANY charge in the field
𝐹Ԧ = 𝑞𝐸
Electric field
• electric field lines
instead of showing force vectors, use
continuous lines with a direction
(field lines)
𝑞
+
𝑞𝑡𝑒𝑠𝑡
for a point charge q: 𝐹 =
so
𝐸=
𝐹
𝑞𝑡𝑒𝑠𝑡
k = 9.0 x 109 N m2/C2
𝑘𝑞𝑞𝑡𝑒𝑠𝑡
𝑟2
𝑘𝑞
𝐸= 2
𝑟
−
Electric field – superposition
• more than just two point charges
The net electric field at a location is the vector sum of all the
individual electric fields from charges
𝐸 = 𝐸1 + 𝐸2 + ⋯
𝐸2
𝐸1
𝐸2
q1
q2
+
+
P
𝐸3
−
𝐸
𝐸1
𝐸3
×
𝐸
q3
Electric field from charge distributions
• applying superposition principle
•
force direction is the tangent to the field line
•
spacing of lines indicates relative strength of the field
•
field lines begin on positive charge and terminate on negative charge
•
the number of field lines from a charge indicates relative size of charge
Electric field
• Now work through the following:
Wolfson Chapter 20
section 20.3
example 20.3
PhysCasts on Canvas (Electric Charge, Force and Field)
Where to Put the 3rd Charge
Three Charges on a Square
PHY10004
Week 1c Essentials
Chapter 20 (cont.)
• electric dipole
• continuous charge distributions
• conductors and insulators
Electric field from a dipole
• a pair of equal but opposites charges
is a common configuration
charges +q and –q
separated by distance d
𝑝Ԧ
Dipole moment: p = qd
d
𝑝Ԧ points from negative to positive
Electric field from a dipole
• quite complicated field variation
field can be calculated reasonably
easily for two cases:
- along the axis of the dipole 𝑥 ≫ 𝑑
2𝑘𝑝Ԧ
𝐸= 3
𝑥
- along the perpendicular bisector 𝑦 ≫ 𝑑
−𝑘𝑝Ԧ
𝐸=
𝑦3
y
x
Electric field for charge distributions
• what about continuous charge distributions?
add the fields from each tiny piece
of the charge distribution
P
𝐸 = ෍ 𝐸𝑖
infinite sum
×
𝑖
𝑘𝑑𝑞
𝐸 = න 𝑑𝐸 = න 2 𝑟Ƹ
𝑟
Matter in electric fields
• field exerts a force on charges
“monopole”
point charge
−
𝐹Ԧ = 𝑞𝐸
𝐹Ԧ net = 𝑚𝑎Ԧ
+
𝐸
𝑞
𝑎Ԧ = 𝐸
𝑚
electric force
Newton’s 2nd
Law
Matter in electric fields
• field exerts a force on charges
𝐹Ԧ = 𝑞𝐸
dipole
𝐹Ԧ net = 𝑚𝑎Ԧ = 0 uniform
field
𝐸
𝜃
forces cancel, but
𝜏 = 𝑟𝐹 sin 𝜃
what about torques?
𝜏net = 𝑞𝑑𝐸 sin 𝜃
𝜏Ԧ = 𝑝Ԧ × 𝐸
Matter in electric fields
• electric force is conservative → potential energy, U
dipole
work done by force 𝑊 = න 𝐹Ԧ ⋅ 𝑑𝑟Ԧ = න 𝜏. 𝑑𝜃
𝑈 = −𝑝Ԧ ∙ 𝐸
change in potential energy
Δ𝑈 = −𝑊
𝐸
+
-
𝑈=0
𝑈>0
𝑈<0
Matter in electric fields
• matter is composed of charged particles (electrons, protons)
depending on the type of matter, these charges respond
differently to an applied electric field
𝐸
conductor
insulator
Matter in electric fields - dielectrics
• matter is composed of charged particles (electrons, protons)
dipoles can exist in some materials
_
+
_
+
_
+
_
+
_
+
𝐸
_
+
_
+
_
+
_
+
dielectric materials are
insulators that can be
polarised by an
external electric field
Dipoles and matter in fields
• Now work through the following:
Wolfson Chapter 20
sections 20.4 and 20.5
examples 20.4 and 20.5