Download Chapters 16 and 17

Chapter 16
Electric Charge and
Electric Field
16.1 Static Electricity; Electric Charge
and Its Conservation
Objects can be charged by rubbing
16.1 Static Electricity;
Electric Charge and Its
Conservation
Charge comes in two
types, positive and
negative; like charges
repel and opposite
charges attract
16.1 Static Electricity; Electric Charge
and Its Conservation
Electric charge is conserved – the
arithmetic sum of the total charge cannot
change in any interaction.
Smallest charge
Charge on electron = - e
Charge on proton = + e
16.2 Electric Charge in the Atom
Atom:
Nucleus (small,
massive, positive
charge)
Electron cloud (large,
very low density,
negative charge)
16.2 Electric Charge in the Atom
Atom is electrically neutral.
Rubbing charges objects by moving electrons
from one to the other.
16.2 Electric Charge in the Atom
Polar molecule: neutral overall, but charge not
evenly distributed
16.3 Insulators and Conductors
Conductor:
Insulator:
Charge flows freely
Almost no charge flows
Metals
Most other materials
Some materials are semiconductors.
16.4 Induced Charge; the Electroscope
Metal objects can be charged by conduction:
16.4 Induced Charge; the Electroscope
They can also be charged by induction:
Ground
Ground =
Infinite sink
Of positive
Or negative
charge
16.4 Induced Charge; the Electroscope
Nonconductors won’t become charged by
conduction or induction, but will experience
charge separation:
16.4 Induced Charge; the Electroscope
The electroscope
can be used for
detecting charge:
16.4 Induced Charge; the Electroscope
The electroscope can be charged either by
conduction or by induction.
16.4 Induced Charge; the Electroscope
The charged electroscope can then be used to
determine the sign of an unknown charge.
Recap E&M
• Thales of Miletus – 600 BC (static
electricity)
• Han Christian Orstead – 1820 (current
and magnetism)
• Michael Faraday (1791-1867) –
Experimentalist
• James Clerk Maxwell (1831-1879) –
Theorist
• Newton’s Laws – Mechanics
• Maxwell’s Equations – E&M
16.5 Coulomb’s Law
Experiment shows that the electric force
between two charges is proportional to the
product of the charges and inversely
proportional to the distance between them.
16.5 Coulomb’s Law
The force between two charges:

Q1Q 2 
F12  k 2  F21
r
This equation gives the magnitude of
the force. Q (or q) represents the
magnitude of the charges and r is the
distance between them.
16.5 Coulomb’s Law
The force is along the line connecting the
charges, and is attractive if the charges are
opposite, and repulsive if they are the same.
16.5 Coulomb’s Law
Unit of charge: coulomb, C
The proportionality constant in Coulomb’s
law is then:
But let' s use k  9  10 N  m /C
9
2
2
Charges produced by rubbing are
typically around a microcoulomb:
16.5 Coulomb’s Law
Charge on the electron:
Electric charge is quantized in units
of the electron charge.
16.5 Coulomb’s Law
The proportionality constant k can also be
written in terms of
, the permittivity of free
space:
(16-2)
Force
•
•
•
•
F α product of two charges
F α 1/r2
FG = - G (m1 m2)/r2
FC = ±k (q1 q2)/r2
• FC / FG for two protons ~ 2x1039
Review
• 2 kinds of charges (+, -)
• Unit = Coulomb (proton, electron =
± 1.6 x 10-19 C = ± e
• Like repel, opposites attract
• Insulators, Conductors
• Charge by rubbing, conduction, induction
16.5 Coulomb’s Law
Coulomb’s law strictly applies only to point charges.
Superposition: for multiple point charges, the forces
on each charge from every other charge can be
calculated and then added as
vectors.
16.6 Solving Problems Involving
Coulomb’s Law and Vectors
The net force on a charge is the vector
sum of all the forces acting on it.
Trig Review
•
•
•
•
SOHCAHTOA
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent

FX  F Cosθ
Vectors in 2-D

F
y

FY  F Sinθ
or

FX  F Sin 

FY  F Cos
φ
θ
x
Vectors in 2-D Part II
• May Define a Vector either as FX and FY
(Requires coordinate system)



F
1
Y
• Or: F and θ where θ  tan 

F 
 X

F
FY
FX
Force Problem - Force on Q4? (16-15)
Q1 = Q3 = +3mC and Q2 = Q4 = -3mC
d = 10 cm
Q1
Q4
d
Q2
Q3
Force Vectors
Q1
F41
F42
Q4
F43
d
Q2
Q3
Solving Vectors
y
F42
F41
θ
F42y
F42x
F41x
F43y
F43
Θ = 450 and F43x = F41y = 0
x
y
F42
F41
θ
F42y
F42x
F41x
F43y
x
OR
  tan
1
F4 y
F4 x
 225
o
y
θ
Q1
d
Q2
Q4

F4
Q3
x
16.7 The Electric Field
The electric field is the
force on a small charge,
divided by the charge:
(16-3)
Electric Field
• Put a small positive test charge (q) in a
region
• Find the force F on that charge
• E = F/q
• Direction of E is direction the positive test
charge moves.
16.7 The Electric Field
For a point charge Q and a test charge q:

Qq
F k 2
r

 F
E 
q

Q
E k 2
r
16.7 The Electric Field
•
•
•
•
Problem solving in electrostatics:
electric forces and electric fields
Draw a diagram; show all charges,
with signs, and electric fields or
forces with directions
Calculate forces or Electric Fields
using Coulomb’s law
Add forces or Electric Fields (using
vector components) to get result
16.8 Field Lines
The electric field can be represented by field
lines. These lines start on a positive charge
and end on a negative charge.
16.8 Field Lines
The number of field lines starting (ending)
on a positive (negative) charge is
proportional to the magnitude of the charge.
The electric field is stronger where the field
lines are closer together.
Line of Charge

16.8 Field Lines
Electric dipole: two equal charges, opposite in
sign:
2 Like Charges
16.8 Field Lines
The electric field between
two closely spaced,
oppositely charged parallel
plates is constant.
16.8 Field Lines
Summary of field lines:
1. Field lines indicate the direction of the
field; the field is tangent to the line.
2. The magnitude of the field is proportional
to the density of the lines.
3. Field lines start on positive charges and
end on negative charges; the number is
proportional to the magnitude of the
charge.
Electric Field Problem 16-34
Q1 = Q2 = Q3 = +2.25 μC and d = 1m
Q1

E ?
d
Q2
Q3
y
E3
Q1
E2
E1
d
Q2
Q3
x

Q
E k 2
r
y
E3
E2
x
E1
= 2.74 x 104 N/C
OR
Q
2
Q
1
E  E  E  k 2 1 
 2k 2 2 
d 
4 
d 
2
2
x
2
y
  tan
1
Ey
Ex
 45
o
y
Q1
E
450
x
d
Q2
Q3
16.11 Electric Forces in Molecular
Biology: DNA Structure and Replication
Molecular biology is the
study of the structure and
functioning of the living cell
at the molecular level.
The DNA molecule is a
double helix:
16.11 Electric Forces in Molecular Biology: DNA
Structure and Replication
The A-T and G-C nucleotide bases attract each other
through electrostatic forces.
16.11 Electric Forces in Molecular
Biology: DNA Structure and Replication
Replication: DNA is in a “soup” of A, C, G, and T in
the cell. During random collisions, A and T will be
attracted to each other, as will G and C; other
combinations will not.
Chapter 17
Electric Potential
Work
W  F// d
If ΔPE increases W is 
If ΔPE decreases W is 
If F  d W is 0 and PE  0
In our case F  qE and W  qE // d
17.1 Electrostatic Potential Energy and
Potential Difference
The electrostatic force is
conservative – potential
energy can be defined
17.1 Electrostatic Potential Energy and
Potential Difference
Electric potential is defined as potential
energy per unit charge:
(17-2a)
Unit of electric potential: the volt (V).
1 V = I J/C.
17.1 Electrostatic Potential Energy and
Potential Difference
Only changes in potential can be measured,
allowing free assignment of V = 0.
(17-2b)
17.1 Electrostatic Potential Energy and
Potential Difference
Analogy between gravitational and electrical
potential energy:
17.2 Relation between Electric Potential
and Electric Field
Work is charge multiplied by potential:
Work is also force multiplied by
distance:
17.2 Relation between Electric Potential
and Electric Field
Solving for the field,
(17-4b)
If the field is not uniform, it can be
calculated at multiple points:
17.3 Equipotential Lines
If V  0, PE  0 and W  0
Therefore E  d
An equipotential is a line or
surface over which the
potential is constant.
Electric field lines are
perpendicular to
equipotentials.
17.3 Equipotential Lines
+
-
Power Supply
Voltmeter
17.5 Electric Potential Due to Point
Charges
The electric potential due to a point charge
can be derived using calculus.
(17-5)
This assumes V = 0 at r = ∞
V for Point Charges
Q
Vk
r
This assumes V = 0
at r = ∞
17.5 Electric Potential Due to Point
Charges
Using potentials instead of fields can make
solving problems much easier – potential is a
scalar quantity, whereas the field is a vector.
Post Spring Break Review
Vectors
Direction – opposites
Attract, like repel

Q
E k 2
r
Direction – follow positive charge
SCALARS
Q
Vk
r
Q1Q 2
PE  k
 Q 2 V1  Q1V2
r
ΔKE = -ΔPE
4 Types of problem for Chapter 17
• 1) V at a point
• 2) Find Potential Energy
• 3) Conservation of Potential and
Kinetic Energy
• 4) Capacitors
1 - Find V for Point Charges
Q1
Q
Vk
r
V=?
3 cm
3 cm
4 cm
Q2
r1  r2  r 
Q1 = Q2 = Q = 6 μC
3 cm  4 cm
2
2
 5 cm
Q1
Q2
Q
Vk
k
 2k
r1
r2
r

V  2 9 10
 2.16 10
9 Nm2
C2
6 Nm
C

 6 10 C 


2

 5 10 m 
6
 2.16 10
6 J
C
Note: V = 0 if Q2 = -6 μC
 2.16 10 V
6
2 -Potential Energy
Q1Q 2
PE  k
 Q 2 V1  Q1V2
r
PE  Work
For a point Charge V = 0 at r = ∞
Potential Energy of a System of
Charges
1
2 cm
2 cm
3
2
2 cm
Q1 = Q2 = Q3 = 2 μC
1st way - Find all combinations of
pairs
PE SYS
Q1Q 3
Q 2Q3
Q1Q 2
k
k
k
r12
r13
r23
Q1Q 2
 3k
r





 2 10 C 2 10 C 


 3 9 10
2
2 10 m


 5.4 N - m  5.4 J
9 N m2
C
6
6
2nd way – Calculate work to build
system
1
3
∞ to 3; W = Q3V2 + Q3V1
∞ to 1; W = 0
2
∞ to 2; W = Q2V1
PESYS  Q2 V1  Q3V2  Q3V1
 kQ1 
 kQ 2 
 kQ1 
 Q2 
  Q3 
  Q3 

 r 
 r 
 r 
PE SYS
Q1Q 3
Q 2Q3
Q1Q 2
k
k
k
r12
r13
r23
3rd Type Conservation of Energy
A (+)
B (-)
VB
VA
VA > VB
E
For + Charge
PEA > PEB
+
-
For - Charge
PEB > PEA
A (+)
B (-)
VB
VA
E
+
VA – VB = 200 V
ΔKE = -ΔPE
KEB- KEA0 = - (PEB – PEA)
KEB = PEA – PEB
KEB = q(VA – VB)
Proton :
q = 1.602 x 10-19 C
m = 1.67 x 10-27 Kg
KEB = q(VA – VB) = (1.602 x 10-19 C)(200V) =
3.2 x 10-17 J
New Energy Unit: The Electron Volt
One electron volt (eV) is the energy gained
by an electron or proton moving through a
potential difference of one volt.
In our case ; If ΔV = 200 V
KEB = 200 eV
If KEB = 3.2 x 10-17 J what is the
proton’s speed?
KE 
1
2
2
mv :

17

2KE
2 3.2 10 J
v

 27
m
1.67 10 Kg
 2 10 m/s
5
17.7 Capacitance
A capacitor consists of two conductors that are
close but not touching. A capacitor has the ability to
store electric charge, create an Electric Field, and
store energy.
ΔV
E
+Q
-Q
17.7 Capacitance
Parallel-plate capacitor connected to battery. (b)
is a circuit diagram.
17.7 Capacitance
When a capacitor is connected to a battery, the
charge on its plates is proportional to the
voltage:
(17-7)
The quantity C is called the capacitance.
Unit of capacitance: the farad (F)
1 F = 1 C/V
17.7 Capacitance
The capacitance does not depend on the
voltage; it is a function of the geometry and
materials of the capacitor.
For a parallel-plate capacitor:
(17-8)
17.8 Dielectrics
A dielectric is an insulator, and is
characterized by a dielectric constant K.
Capacitance of a parallel-plate capacitor filled
with dielectric:
(17-9)
17.8 Dielectrics
Dielectric strength is
the maximum field a
dielectric can
experience without
breaking down.
17.8 Dielectrics
The molecules in a dielectric tend to become
oriented in a way that reduces the external
field.
17.8 Dielectrics
This means that the electric field within the
dielectric is less than it would be in air,
allowing more charge to be stored for the
same potential.
17.9 Storage of Electric Energy
A charged capacitor stores electric energy;
the energy stored is equal to the work done
to charge the capacitor.
(17-10)
17.7 Energy
ΔV
+Q
E
-Q
17.9 Storage of Electric Energy
The energy density, defined as the energy per
unit volume, is the same no matter the origin of
the electric field:
(17-11)
The sudden discharge of electric energy can be
harmful or fatal. Capacitors can retain their
charge indefinitely even when disconnected
from a voltage source – be careful!
17.9 Storage of Electric Energy
Heart defibrillators use electric
discharge to “jump-start” the
heart, and can save lives.
Capacitors one more time
Both capacitors get charged fully but keep C1
Connected to battery and disconnect C2
Keep C1 Attached to Battery
V is constant
Add a dielectric K and what
Happens to C, Q, PE, E
C  Q
PE 
E unchanged
so  = K0
Remove C2 from the Battery
Q is constant
Add a dielectric K and
what
Happens to C, V, PE, E
C
PE 
V
E
17.10 Cathode Ray Tube: TV and
Computer Monitors, Oscilloscope
A cathode ray tube
contains a wire cathode
that, when heated, emits
electrons. A voltage
source causes the
electrons to travel to the
anode.
17.10 Cathode Ray Tube: TV and
Computer Monitors, Oscilloscope
The electrons can be steered using electric or
magnetic fields.
17.10 Cathode Ray Tube: TV and
Computer Monitors, Oscilloscope
Televisions and computer monitors (except for
LCD and plasma models) have a large
cathode ray tube
as their display.
Variations in the
field steer the
electrons on their
way to the screen.
17.10 Cathode Ray Tube: TV and
Computer Monitors, Oscilloscope
An oscilloscope displays en electrical signal on
a screen, using it to deflect the beam vertically
while it sweeps horizontally.
17.11 The Electrocardiogram (ECG or EKG)
The electrocardiogram
detects heart defects by
measuring changes in
potential on the surface
of the heart.
Summary of Chapter 16
• Two kinds of electric charge – positive and
negative
• Charge is conserved
• Charge on electron:
• Conductors: electrons free to move
• Insulators: nonconductors
Summary of Chapter 16
• Charge is quantized in units of e
• Objects can be charged by conduction or
induction
• Coulomb’s law:
• Electric field is force per unit charge:
Summary of Chapter 16
• Electric field of a point charge:
Q
Ek 2
r
• Electric field can be represented by electric
field lines
• Static electric field inside conductor is zero;
surface field is perpendicular to surface
Summary of Chapter 17
• Electric potential energy:
• Electric potential difference: work done to
move charge from one point to another
• Relationship between potential difference
and field:
Summary of Chapter 17
• Equipotential: line or surface along which
potential is the same
• Electric potential of a point charge:
• Electric dipole potential:
Summary of Chapter 17
• Capacitor: nontouching conductors carrying
equal and opposite charge
•Capacitance:
• Capacitance of a parallel-plate capacitor:
Summary of Chapter 17
• A dielectric is an insulator
• Dielectric constant gives ratio of total field to
external field
• Energy density in electric field: