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Electrostatics
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
1
Electrostatics: Coulomb’s Law
The MAN: Charles Augustin de Coulomb
The MAN: Charles Augustin
de Coulomb
He was born in 1736 in Angoulême, He
was born in 1736 in Angoulême
France.
He received the majority of his higher He
received the majority of his higher
education at the Ecole du Genie at Mezieres (sort of the French equivalent of universities like Oxford, Harvard, etc.) from ,
,
)
which he graduated in 1761.
He then spent some time serving as a military engineer in the West Indies and other French outposts, until 1781 when he was permanently stationed in Paris and was able to devote more time to scientific research. Between 1785‐91 he published seven memoirs (papers) on physics.
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Electrostatics: Coulomb’s Law
The INSTRUMENT: The torsion balance
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Coulomb’s torsion balance
and how it works
how it works
 Coulomb used a torsion balance to measure electrostatic force.
electrostatic force.  Inside the balance are two pith balls. One is mounted on the end of a glass rod and is unmovable (red), the other can spin around (blue).  When the two pith balls are given an electrostatic charge (charging a plastic rod by rubbing it with fur
charge (charging a plastic rod by rubbing it with fur then touching that rod to the pith ball) the mobile ball will move away from the stationary one if both receive the same charge (positive or negative); or will move towards the unmovable ball, if each is given a different charge The distance the mobile ball moves
different charge. The distance the mobile ball moves is used to measure the electrostatic force.  Coulomb was able to measure the torsion on the fiber with the scale near the top of the device and the pp
distance between the balls on the scale wrapped around the base of the jar. He derived a mathematical d h b
f h j H d i d
h
i l
equation that described the relationship between these two measurements.  Coulomb’s
Coulomb s Law states: The force between two Law states: The force between two
small charged spheres is proportional to the magnitude of either charge and inversely proportional to the square of the distance e ee e e
between centers.
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Coulomb’s law
Coulomb’s Law: The magnitude of the force between two point charges is proportional to the h
i
ti
l t th
product of their charges and inversely proportional to the
inversely proportional to the square of their separation.
‐12
2 ‐1 ‐2 = 8.854 x 10
C
N m “electric permittivity”
0
9 ‐2
9 2
k
k = 8.988 x 10
C 2Nm2 k = 1/4π
1/4 0
Measured charge on the electron: e = 1.6 x 10‐19 C
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Coulomb’ss Law
Coulomb
Law
Formula
Where F is the force between the two particles a and b, qa and qb are g
p
,
the charges on particles a and b, r is the distance between a and b, and k is the Coulomb’s constant 8.99x109 (Nm2/C2).
If you have more than two charged particles the force on one would be the sum of the forces acting on it due to the other two particles, but not including the forces the other two have on each i l b
i l di
h f
h
h
h
h
other.
Total Force on particle C = Force on C due to A + Force on C due to B
T
t lF
ti l C F
Cd t A F
Cd t B
Fc = Fca + Fcb
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Electric Field
Electric Field
The electric force is a field force, it applies force without The
electric force is a field force it applies force without
touching (like the gravitational force)
In the region around a charged object, an Electric Field is said to exist
is said to exist
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Electric Field
Electric Field
Rules for Drawing Electric Field Lines
l f
i
l
i i ld i
1. The lines must originate on a positive charge (or infinity) and end on a negative charge (or infinity).
2. The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge.
ti
l t th
it d f th h
3. No two field lines can cross each other.
4. The line must be perpendicular to the surface of the charge
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Electric Field
Electric Field
Electric field
l
i fi ld
• Space surrounding an electric charge (an energetic aura)
• Describes electric force
• Around a charged particle obeys inverse‐square law
p
g
• Force per unit charge
Electric Field
Electric Field
Electric field direction
• Same direction as the force on a positive charge
p
g
• Opposite direction to the force on an electron
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics

 F E
E
q0
•
•
•
•
•
•
Electric Field
Electric Field
becomes
q
E  kc 2
r
E  electric field strength, N/C  VECTOR
q0  + test charge, C
+ test charge C
q  charge producing field, C
r  distance between charges, m
r 
distance between charges m
FE  Electric Force, N  VECTOR
kc coulomb constant, 8.99x10
coulomb constant 8 99x109Nm2/C2
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
E Field vs g‐field
E‐Field vs
g field
E  Field

 F0
E
q0
g  field

 Fg
g
m0
Coulomb’ss Law
Coulomb
Law
Differences between gravitational and electrical forces
• Electrical forces may be either attractive or repulsive.
• Gravitational forces are only attractive.
y
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
E Field
E‐Field

E
1
q
ˆ
r
2
4 0 r
Electric Potential
Electric Potential
Electric potential energy
• Energy possessed by a charged particle due to its gy p
y
g p
location in an electric field. Work is required to push a charged particle against the electric field of a g p
g
charged body.
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Electric Potential
Electric Potential
(a) The spring has more elastic PE when compressed. (b) The small charge similarly has more PE when pushed closer to the charged sphere. In both cases, the increased PE is the result of
the increased PE is the result of work input.
Electric Potential
Electric Potential
Electric potential (voltage)
• Energy per charge
gy p
g p
possessed by a charged particle y
g p
due to its location
May be called voltage—potential
potential energy per charge
energy per charge
• May be called voltage
• In equation form: Electric potential  electric potential energy
Electric potential amount of charge
Electric Potential
Electric potential (voltage) (continued)
• Unit of measurement: volt, 1 volt 
1 joule
1 coulomb
Example:
• Twice the charge in same location has twice the electric potential energy but the same electric potential.
• 3 times the charge in same location has 3 times the electric potential energy but the same electric potential (2 E/2 q = 3 E/3 q
energy but the same electric potential (2 E/2 q
3 E/3 q = V)
V)
Electric Potential
Electric potential (voltage) (continued)
Electric potential (voltage) (continued)
• High voltage can occur at low electric potential energy for a small amount of charge
for a small amount of charge.
• High voltage at high electric potential energy occurs for lots of charge
lots of charge.
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Electric Energy Storage
• Electrical energy can be stored in a common device called a capacitor
common device called a capacitor.
• The simplest capacitor is a pair of conducting plates separated by a d ti
l t
t db
small distance, but not touching each other. h th
• When the plates are connected to a charging device, such as the battery, electrons are transferred from one plate to the other.
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Electric Energy Storage
• This occurs as the positive battery terminal pulls electrons from the plate connected to it.
p
• These electrons, in effect, are pumped through the battery and through the negative terminal to the
battery and through the negative terminal to the opposite plate.
• The capacitor plates then have equal and opposite The capacitor plates then have equal and opposite
charges:
– The
The positive plate connected to the positive battery terminal, positive plate connected to the positive battery terminal
and
– The negative plate connected to the negative terminal. The negative plate connected to the negative terminal
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Electric Energy Storage
• The charging process is complete when the potential difference between the plates equals the potential p
q
p
difference between the battery terminals—the battery voltage. g
• The greater the battery voltage, and the larger and closer the plates, the greater the charge that can be
closer the plates, the greater the charge that can be stored.
• The energy stored in a capacitor comes from the work The energy stored in a capacitor comes from the work
required to charge it. • Discharging a charged capacitor can be a shocking Di h i
h
d
it
b
h ki
experience if you happen to be the conducting path. P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Electric Energy Storage
• A common laboratory device for producing high voltages and creating static electricity is the Van de Graaff generator.
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Conductors in Electrostatic Equilibrium
Conductors in Electrostatic Equilibrium
1 Th
1.
The electric field is zero everywhere inside a l t i fi ld i
h
i id
conductor.
2 Any excess charge on an isolated conductor resides 2.
Any excess charge on an isolated conductor resides
entirely on the outside surface of the conductor.
3. The electric field just outside the charged The electric field just outside the charged
conductor is perpendicular to the conductor’s surface.
4. On an irregularly shaped conductor, charge tends to accumulate where the radius of curvature is the smallest i e AT SHARP POINTS
smallest, i.e. AT SHARP POINTS.
Electrostatics: Coulomb’s Law
Electric field
Electric field
1) Imagine a single charged particle. Charged particles around it will either move directly toward it or directly away from it. In thi
this way, we illustrate the ill t t th
electric field lines as emanating radially from the charged particle
the charged particle.
2) Imagine a sheet of charged particles: the E‐field will be perpendicular to the
be perpendicular to the surface.
Charged particles and http://www.colorado.edu/physics/PhysicsInitiative/Physics2000.05.98/applets/nforcefield.html
force fields : http://www.colorado.edu/physics/PhysicsInitiative/Physics2000.05.98/waves_particles/wavpart3.html
http://www.colorado.edu/physics/2000/waves_particles/wavpart2.html
Electric fields: http://www.mrfizzix.com/utilitypage/dukes/electricfield/ElectricField.htm
Electric fields:
htt //
fi i
/ tilit
/d k / l t i fi ld/El t i Fi ld ht
http://physics.weber.edu/amiri/director/DCRfiles/Electricity/efiel24s.dcr
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Electrostatics: Coulomb’s Law
How a photocopier works
Working components of a photocopier
Working components of a photocopier
Photoreceptor drum (or belt) Corona wires
Lamp and lenses
Lamp and lenses
Toner
Fuser
A drum is basically a metal roller covered by a layer of photoconductive
material. This layer is made out of a semiconductor
t i l Thi l
i
d
t f
i d t such as selenium, germanium h
l i
i
or silicon. What makes elements like selenium so cool is that they can conduct electricity in some cases, but not in others. In the dark, the photoconductive layer on the drum acts as an insulator resisting the flow of electrons from one atom to
on the drum acts as an insulator, resisting the flow of electrons from one atom to another. But when the layer is hit by light, the energy of the photons liberates electrons and allows current to pass through! These newly freed electrons are what neutralizes the positive charge coating the drum to form the latent image
what neutralizes the positive charge coating the drum to form the latent image. P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Electrostatics: Coulomb’s Law
How a photocopier works
Working components of a photocopier
Working components of a photocopier
Photoreceptor drum (or belt)
Corona wires
Lamp and lenses
Lamp and lenses
Toner
Fuser
For a photocopier to work, a field of positive charges must be generated on the surface of both the drum and the copy paper.
th
f
f b th th d
d th
Th
These tasks are t k
accomplished by the corona wires. These wires are subjected to a high voltage, which they subsequently transfer to the drum and paper in the form of static electricity. electricity
One of these wires is stretched parallel to the drum surface and charges the photoconductive surface with positive ions, and the other wire is positioned to coat the paper'ss surface as the paper shoots by on its way to the drum. coat the paper
surface as the paper shoots by on its way to the drum
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Electrostatics: Coulomb’s Law
How a photocopier works
Working components of a photocopier
Working components of a photocopier
Photoreceptor drum (or belt)
Corona wires
Lamp and lenses
Lamp and lenses
Toner
Fuser
Making a photocopy requires a light source with enough energy to boot electrons out of the semiconductive coating on the drum (also called a photoconductor, is this case). What wavelengths of light can do this? It turns out that most of the visible spectrum of light contains enough energy to drive the process, especially the green and blue end of the spectrum. Anything lower than the red portion of the visible spectrum doesn't have enough energy to activate the h
d
i
f h i ibl
d
' h
h
i
h
photoconductor. And, although UV light has more than enough firepower to make a photocopy, it can be very damaging to our eyes and skin. This is why photocopiers use a plain old incandescent
h t
i
l i ld i
d
t or fluorescent bulb to flash light onto fl
t b lb t fl h li ht t
the original document.
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Electrostatics: Coulomb’s Law
How a photocopier works
Working components of a photocopier
Photoreceptor drum
Photoreceptor
drum (or belt)
(or belt)
Corona wires
Lamp and lenses
Toner
Fuser
Toner is sometimes referred to as dry ink, but toner isn
Toner
is sometimes referred to as dry ink, but toner isn'tt actually ink at all! actually ink at all!
Ink is a pigmented liquid. Toner is a fine, negatively charged, plastic‐based powder. The black color in photocopier toner comes from pigments blended into the plastic pa c es
particles while they are being made. e ey a e be g ade
Toner is stuck on larger, positively charged beads and stored inside a toner cartridge. When toner‐coated beads are rolled over the drum, the toner particles find the positively charged ions on the unexposed areas on the drum's surface attractive.
The same particles are subsequently even more drawn to the electrostatically charged paper. The plastic in the toner lets you keep it from jumping ship once you've finally got it on the paper; all you have to do is apply heat to the toner, and the plastic particles melt and fuse the pigment to the paper. P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Xerography: uses photoconductive material coating(Selenium) a drum
P.Ravindran, PHY041: Electricity & Magnetism 08 January 2013: Electrostatics
Millikan Oil-Drop
p Experiment
p
Millikan Oil
Oil-Drop
Drop Experiment
• Robert Millikan measured e, the charge of the electron e = 1.60 x 10‐19 C
• He
He also demonstrated the quantized nature of also demonstrated the quantized nature of
this charge
Oil-Drop
Oil
Drop Experiment
• With no electric field between the plates:
The drop reaches terminal velocity with FD = mg
Oil-Drop
p Experiment
p
• When an electric field is set up between the plates the p
p
drop moves upwards and reaches a new terminal velocity velocity
= mg +FD =qE
• Fe = mg +F
• Solve
Solve for q
for q
•
Observed thousands of times and always found e=multiple of 1.6x10‐19 C