Electrostatics
GIRL SAFELY CHARGED TO
SEVERAL HUNDRED
THOUSAND VOLTS
GIRL IN GREAT DANGER AT
SEVERAL THOUSAND VOLTS
The Nature of Electric Charge
Discovery of charge
The Greeks first noticed electric charged by
rubbing amber with fur, then picking up bits of
matter. The Greek word for amber is elektron.
Benjamin Franklin arbitrarily called the two
kinds of charge positive and negative. In most
cases, only the negative charge is mobile.
Properties of charge
Like charges repel, and unlike charges
attract.
Charge is conserved, meaning it cannot be
created or destroyed, only transferred from
one location to another.
In all atoms, electrons (qe) have negative charge
and protons (qp) have positive charge.
Charge is quantized, meaning it comes in
discrete amounts (like money).
total charge = integer x fundamental unit of charge
click for
animation
Insulators and Conductors
Insulators
In insulators, electrons are bound in
“orbit” to the nucleus in each atom.
When charge is placed on an insulator, it
stays in one region and does not distribute.
Wood, plastic, glass, air, and cloth
are good insulators.
Conductors
In conductors electrons can move from
atom to atom, thus electricity can “flow”.
CHARGED INSULATOR
When charge is placed on a conductor, it
redistributes to the outer surface.
Metals (copper, gold, and aluminum)
are good conductors.
CHARGED CONDUCTOR
Polarization
Polarization is the separation of charge
In a conductor, “free” electrons can move around the surface of
the material, leaving one side positive and the other side negative.
In an insulator, the electrons “realign” themselves within the
atom (or molecule), leaving one side of the atom positive and
the other side of the atom negative.
Polarization is not necessarily a charge imbalance!
Charging by Friction
POSITIVE
Rabbit's fur
Glass
Mica
Nylon
Wool
Cat's fur
Silk
Paper
Cotton
Wood
Lucite
Wax
Amber
Polystyrene
Polyethylene
Rubber ballon
Sulfur
Celluloid
Hard Rubber
Vinylite
Saran Wrap
NEGATIVE
When insulators are rubbed together, one
gives up electrons and becomes positively
charged, while the other gains electrons
and becomes negatively charged.
Materials have different affinities for
electrons. A triboelectric series rates this
relative affinity.
A material will give up electrons to
another material below it on a
triboelectric series.
Common examples of charging by friction:
• small shocks from a doorknob after walking
on carpet with rubber-soled shoes
• plastic foodwrap that sticks to a container
• sweater pulled over your head that sparks
• laundry from the dryer that clings
• balloon rubbed with hair sticks that to a wall
click for applet
Charging by Conduction
When a charged conductor makes contact with a
neutral conductor there is a transfer of charge.
CHARGING NEGATIVELY
CHARGING POSITIVELY
Electrons are transferred from
the rod to the ball, leaving them
both negatively charged.
Electrons are transferred from
the ball to the rod, leaving
them both positively charged.
Remember, only electrons are free to move in solids.
Notice that the original charged object loses some charge.
click for
animation
Charging by Induction
Induction uses the influence of one charged object to
“coerce” charge flow.
Step 1. A charged rod is brought
near an isolated conductor. The
influence of the charge object
polarizes the conductor but does
not yet charge it.
Step 2. The conductor is
grounded to the Earth,
allowing charge to flow out
between it and the Earth.
Charging by Induction (cont.)
Step 3. The ground is removed
while the charge rod is still
nearby the conductor.
Step 4. The rod is removed
and the conductor is now
charge (opposite of rod).
An object charged by induction has the opposite sign
of the influencing body.
Notice that the original charged object does not lose charge.
click for
animation
click for
animation
click for
animation
Electric Forces and Electric Fields
CHARLES COULOMB
(1736-1806)
MICHAEL FARADAY
(1791-1867)
Electrostatic Charges
A New Fundamental Physics Quantity
Electrostatic charge is a
fundamental quantity like
length, mass, and time.
The symbol for charge is q.
The SI unit for charge is
called the coulomb (C).
ATTRACTION AND REPULSION
The charge of an electron (qe) is -1.6 x 10-19 C
The charge of an proton (qp) is 1.6 x 10-19 C
Common electrostatic charges are small:
millicoulomb = mC = 10-3 C
microcoulomb = C = 10-6 C
nanocoulomb = nC = 10-9 C
The Electrostatic Force
Charles Coulomb’s Torsion Balance
A torsion balance measures the
force between small charges.
The electrostatic force depends directly
on the magnitude of the charges.
The force depends inversely on the
square of distance between charges
(another “inverse square law”)!
COULOMB’S LAW OF
ELECTROSTATIC FORCE
constant
charges
kq1q2
Fe  2
r
electrostatic
force
distance
TORSION BALANCE
The constant of proportionality, k,
is equal to 9.0 x 109 Nm2/C2.
A negative force is attractive,
and a positive force is repulsive.
The sign (+ or –) is different from
a vector direction (left or right)
The Electrostatic Force
EXAMPLE 1 - Find the force between these two charges
9.0  10 5  10


9
Fe
6

C 8  10 6 C
0.04 m 2

Fe  225 N
The negative signs means force of attraction,
but does not indicate left or right direction
EXAMPLE 2 - Find the net force on the left charge
9.0  10 5  10


9
Fe
Fe  360 N
6

C 5  10 6 C
0.025 m 2

(force of repulsion)
Fnet  Fleft  Fright
Fnet  360 N  225 N  135 N, to the left
The Electrostatic Force
EXAMPLE 3 - Find the net force on the upper left charge
Fe,x  225 N, right
Fe,y  360 N, up
Fe  Fe,x 2  Fe,y 2  225 2  360 2  425 N
 Fe,y 
1  360 
  tan 

tan

  58.0Þ

225
 Fe,x 
1
425 N,
58˚
EXAMPLE 4 (Honors only) - Find the net force on the lower left charge
9.0  10 5  10 C–8  10 C  162
9
Fe1 
-6
-6
0.04  0.025 m
2
2
Fe1,x  162 cos 32Þ 137.2 N
 2.5 
  tan -1 
 32Þ
 4 
Fe1,y  162 sin 32Þ 85.75 N
Fe  Fe,x 2  Fe,y 2  137.2 2  (85.75  360)2  307 N
307 N,
-63.4˚
 Fe,y 
1  85.75  360 

tan

  63.4Þ

137.2 
 Fe,x 
  tan 1 
Electric Field Strength
Field Theory Visualizes Force At A Distance
DEFINITION OF
GRAVITATIONAL
FIELD
DEFINITION OF
ELECTRIC
FIELD
force
g field 
mass
g
E field 
force
charge
Fe
E
q0
Fg
m
q0 is a small, positive test charge
Electric field is a vector quantity
E field points toward negative charges
E field points away from positive charges
SI unit of electric field
click for
applet
newton
N

coulomb C
Electric Field Lines
Single Point Charges
POSITIVE CHARGE
NEGATIVE CHARGE
Density of field
lines indicates
electric field
strength
Inverse square
law obeyed
click for applet
Definition of E Field for single point charge
Fe kq0 q / r 2
E

q0
q0
electric
field
constant
charge
kq
E 2
r
distance
Electric Field Lines
Electric fields for multiple point charges
click for
applet
click for
applet
click for
applet
POSITIVE AND NEGATIVE POINT CHARGES
TWO POSITIVE POINT CHARGES
OPPOSITE MAGNETIC POLES
ALIKE MAGNETIC POLES
Electric Fields
EXAMPLE 1
Find the electric field strength at 2 meters
from the 5 millicoulomb charge.
kq
E 2
r
E
9  10

E
9

Nm 2 /C2 5  10 3 C
2 m 2

E=1.13 107 N/C, to the right
EXAMPLE 2
Find the force on an proton placed 2 meters from the
5 millicoulomb charge in the problem above.
E
Fe
q
9  10

F 
e



Fe  qE  1.6  10-19 C 1.13  10 7 N/C  1.81  10-12 N, to the right
9


OR
Nm 2 /C2 5  10 3 C 1.6  10-19 C
2 m 
2
  1.8  10
-12
N, to the right
Electric Potential Energy
Electric Potential Energy versus Gravitational Potential Energy
FALLING MASS VS. FALLING CHARGE
Electric potential energy (PE) is
stored when a positive charge is
moved against an electric field.
Potential energy can be converted to
kinetic energy, heat, light, sound etc.
Potential energy is a scalar
quantity measured in joules (J).
STORING POTENTIAL ENERGY
POTENTIAL ENERGY GAIN OR LOSS
positive (+)
charge
negative (–)
charge
toward E
loses PE
gains PE
opposite E
gains PE
loses PE
PE for Constant Electric Field
CONSTANT GRAVITATIONAL FIELD
CONSTANT ELECTRIC FIELD
PE  mgh
PE  qEd
Example
electric
potential
energy charge
E field
How much potential energy is converted when an electron is
accelerated through 0.25 m in a cathode ray tube (TV set)
with an electric field strength of 2 x 105 N/C?
PE  qEd  (1.6  1019 ) (2  105 )(0.25)  8.0  1015 J
distance
PE for Two Point Charges (Honors only)
Potential Energy is force times distance
kq1q2
PE  Fe d  2  r
r
electric
potential
energy
constant
charges
kq1q2
PE 
r
distance
Potential energy is positive for like charges
Potential energy is negative for opposite charges
Potential energy is zero at infinite distance
Example
How much electrostatic potential energy in a hydrogen atom, which consists of one
electron at a distance of 5.3 x 10-11 meters from the nucleus (proton).
kq1q2 (9  10 9 )(1.6  10 19 )(–1.6  10 19 )
18
PE 


4.35

10
J
11
r
5.3  10
Potential Difference (Voltage)
Electric potential is average energy per charge.
Energy
Potential 
Charge
Energy is a relative quantity (absolute energy
doesn’t exist), so the change in electric potential,
called potential difference, is meaningful.
PE
A good analogy: potential is to temperature, as
V 
potential energy is to heat.
q
Potential difference is often called voltage.
Voltage is only dangerous when a
lot of energy is transferred.
click for web page
SI Units
Voltage, like energy, is a scalar.
A volt (v) is the unit for voltage
named in honor of Alessandro Volta,
inventor of the first battery.
1 joule
J
1 volt 
V
1 coulomb
C
source
voltage (V)
common dry cell
1.5
car battery
12
household (US)
120
comb through hair
500
utility pole
4,400
transmission line
120,000
Van de Graaff
400,000
lightning
1,000,000,000
Potential Difference (Voltage)
A SEVERAL THOUSAND VOLT POWERLINE
CAN ILLUMINATE A FLUORESCENT LIGHT
A PARACHTUE ACCIDENT LANDED THIS
MAN ON A 138,000 THOUSAND VOLT LINE,
BUT HE SUFFERED ONLY MINOR BURNS
Potential Difference for Constant Electric Field
Potential energy is often stored in a capacitor.
Capacitors are made by putting an insulator
in between two conductors.
Most capacitors have constant electric fields.
PE qEd
V 

q
q
V  Ed
voltage
E field
distance
Example
Calculate the magnitude of the electric field set up in a
2-millimeter wide capacitor connected to a 9-volt battery.
V  Ed  9  E(0.002)  E  4500 N/C
Potential Difference for Point Charge (Honors only)
Consider a test charge to
measure potential
PE kqq0 / r
V

q0
q0
constant
potential
difference
charge
kq
V 
r
distance
Example
-4 nC
0.3 m
find ∆V
here
0.4 m
10 nC
6 nC
kq1 (9  10 9 )(6  10 9 )
V1 

 180 V
r
0.3
kq2 (9  10 9 )(4  10 9 )
V2 

 90 V
r
0.4
kq3 (9  10 9 )(10  10 9 )
V3 

 180 V
r
0.5
V  V1  V2  V3  180  90  180  270 V
Summary of Electrostatic Equations
Electrostatic Force
kq1q2
Fe  2
r
force between two charges
Electric Field
Fe
E
q0
definition
kq
E 2
r
for point charge
Potential Energy
PE  qEd
for constant E field
kq1q2
PE 
r
Honors only!
for two charges
Potential Difference
PE
V 
q
kq
V 
r
definition
for point charge
V  Ed
for constant
E field