Electrostatics: Coulomb’s Law
The MAN: Charles Augustin de Coulomb
He was born in 1736 in Angoulême,
France.
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.
Electrostatics: Coulomb’s Law
The INSTRUMENT: The torsion balance
Coulomb’s torsion balance
and how it works
Coulomb used a torsion balance to measure
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 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 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
distance between the balls on the scale wrapped
around the base of the jar. He derived a
mathematical equation that described the
relationship between these two measurements.
Coulomb’s 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 between centers.
Coulomb’s Law
Formula
Where F is the force between the two particles a and b, qa and qb are
the charges on particles a and b, r is the distance between a and b,
and k is the 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 other.
Total Force on particle C = Force on C due to A + Force on C due to B
Fc = Fca + Fcb
Electrostatics: Coulomb’s Law
The FINDING
A cheat-sheet for electrostatics 4pe0 = 9.00 × 109 Nm2/C2:
Point charge
Charge
between
sheets
Charge dipole
3
Potential V or J/C
q1/4pe0r
V
q1l cos q/4pe0r
1
Field V/m or J/Cm
E = d[v(r)]/dr
q1/4pe0r2
V/d
q1l cos q/4pe0r2
Force N or J/m
q1q2/4pe0r2
Coulomb’s law
qV/d
q1q2l cos q/4pe0r2
Work J
q1q2/4pe0r
qV
q1q2l cos q/4pe0r
2
4
W = ∫[F(r)]dr
q2
q1
q
d
Electrostatics: Coulomb’s Law
Electric field
1) Imagine a single charged
particle. Charged
particles around it will
either move directly
toward it or directly
away from it. In this
way, we illustrate the
electric field lines as
emanating radially from
the charged particle.
2) Imagine a sheet of
charged particles: the Efield will 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
http://physics.weber.edu/amiri/director/DCRfiles/Electricity/efiel24s.dcr
Electrostatics: Coulomb’s Law
How a photocopier works
Working components of a photocopier
Photoreceptor drum (or belt)
Corona wires
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 such
as selenium, germanium 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 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.
Electrostatics: Coulomb’s Law
How a photocopier works
Working components of a photocopier
Photoreceptor drum (or belt)
Corona wires
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. These tasks
are 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.
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's surface as the paper shoots by on its way to
the drum.
Electrostatics: Coulomb’s Law
How a photocopier works
Working components of a photocopier
Photoreceptor drum (or belt)
Corona wires
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 gusto to activate the 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
or fluorescent bulb to flash light onto the original document.
Electrostatics: Coulomb’s Law
How a photocopier works
Working components of a photocopier
Photoreceptor drum (or belt)
Corona wires
Lamp and lenses
Toner
Fuser
Toner is sometimes referred to as dry ink, but toner isn't 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 particles while they are being made.
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.
Electrostatics: Coulomb’s Law
The test!!
At a toner-drum distance of 1 cm, how much electrical charge
will you need on the toner and drum to lift the particle that
distance?