A color xerographic copier isn’t
all that much more complicated than a black and white one. It simply combines four
different colored toners on a single sheet of paper to create full color
images. The fact that only four toners are needed to make us see all the
possible colors is a consequence of our simple color vision; our eyes really
only detect three different types of light (red, green, and blue) and our
brains interpret various mixtures of those three lights as different colors. To
make use of this fact, three of the toners are designed to block particular
types of light (one toner blocks red light, one blocks green light, and one
blocks blue light). The fourth toner is simply black and helps to improve the
contrast of the finished copies.
We will
examine color vision more carefully when we look at Television and Fluorescent
Lamps. For the present problem, you only need to know that the color copier is
trying to detect how much red light, how much green light, and how much blue
light there is coming off the original document. The cheapest color xerographic
system exposes the same photoconductor drum to light from the document four
separate times: once through a filter that passes only red light, once through
a filter that passes only green light, once through a filter that passes only
blue light, and once without any filter at all. The first pass determines where
to place red-absorbing toner, the second pass places green-absorbing toner, the
third pass places blue-absorbing toner, and the last pass places black toner.
These four toner images are superimposed on the paper and create a full color
image.
1. Before the first pass (the one that uses red-filtered light to control the placement of red-absorbing toner), the photoconductor drum is covered with positive electric charge. This charge comes from a thin wire (a corotron) that is held at a high positive voltage of 10,000 volts. Charges leave this wire via a corona discharge and stick to the nearby drum surface. As these positive charges stick, the voltage of the photoconductor surface increases. However, it never exceeds 10,000 volts. Why not?
Answer: For the voltage on the photoconductor surface were to exceed
10,000 volts, something would have to do work on the (positive) charge to
transfer it from the thin wire to the photoconductor surface and there isn't
anything to do that work.
Why: (Positive) charge naturally flows from higher voltage to
lower voltage and releases electrostatic potential energy in the processes.
Charge can't spontaneously flow from lower voltage to higher voltage because
that would mean that its electrostatic potential energy rises. Without a source
of energy, such a rise would violate conservation of energy.
2. The photoconductor surface is supported by a metal cylinder that’s connected by a wire to the earth. Since the voltage of the earth is zero, the cylinder and the inside surface of the photoconductor drum are also always at zero volts. That’s true even though negative charges flow through the cylinder and onto the inner surface of the photoconductor as positive charges land on the outer surface of the photoconductor Once the photoconductor is fully charged, its outside surface has a voltage of 10,000 volts and its inside surface has voltage of 0 volts. A small patch of the photoconductor is then exposed to red light from a document and 0.000001 coulomb (one millionth of a coulomb) of charge crosses from the outside surface to the inside surface of the photoconductor. How much potential energy is released when this charge moves? (This question involves a simple calculation and a quantitative answer. For simplicity, assume that the voltages of surfaces aren’t changed by the transfer of charge.)
Answer: 0.01 joules of energy are released.
Why: Voltage measures the electrostatic potential energy per unit
of charge. In this case, there are 0.000001 coulombs of charge having 10,000
volts (10,000 joules per coulomb) of voltage. If that quantity of charge is
permitted to release all of its electrostatic potential energy and drop to 0
volts, then 0.000001 coulombs times 10,000 joules per coulomb will be released.
That product yields 0.01 joules, which is the amount of energy that will be
released when the charge is permitted to cross through the photoconductor.
3. A color copier’s photoconductor must respond to red light while the photoconductor in a black & white copier can and usually does ignore red light. What must be different about the arrangement of quantum levels in the color copier’s photoconductor as compared to that in the black & white copier?
Answer: The color copier's photoconductor must have a small
energy difference between the filled valence levels and the empty conduction
levels. In the black & white copier, the energy difference can be larger.
Why: For the color copier's photoconductor to respond to red
light, with its low photon energy, the energy required to shift an electron
from a valence level to a conduction level must be relatively small. The bands
of levels must be relatively close in energy. But since the black & white
copier's photoconductor doesn't have to respond to red light, it can have a
wider energy separation between its valence levels and its conduction levels.
4. A copier inevitably places some toner where it doesn’t belong or omits it from where it does belong. This effect is partly the result of thermal energy. The hotter the environment, the more mistakes the copier will make. Fortunately, it has to be pretty hot before the thermal mistakes are noticeable. (a) How does thermal energy cause the copier to make mistakes and (b) why is the photoconductor used in a color copier more vulnerable to these thermal mistakes than the photoconductor used in a black & white copier?
Answer: (a) Thermal energy can shift an electron from a valence level to a conduction level and allow the photoconductor to conduct charge. (b) The small energy separation between the valence and conduction bands in the color copier's photoconductor makes it easier for thermal energy to shift an electron from a valence to a conduction level and cause conduction.
Why: Both light and thermal energy are capable of shifting
electrons from valence levels to conduction levels in a semiconductor. The
closer the valence levels are to the conduction levels, the more easily thermal
energy can cause this sort of shift. Once it occurs, the photoconductor is able
to conduct a small amount of electric current. That's why overheating a
photoconductor/semiconductor is usually a bad idea.
You have an old magnetic compass, which has kept
you from getting lost in the woods many times. Its red-painted end contains a
north magnetic pole and reliably points north, except when there are other
magnetic things around. Its white-painted end contains a south magnetic pole.
5. Suppose that you were walking through the woods and came upon an isolated north magnetic pole of considerable strength. Which end of your compass would point toward that north pole? Use the relationship between total potential energy and acceleration to explain why that particular end points toward the north pole.
Answer: (Optional background: when opposite poles move toward
one another, the forces between them do work and they release magnetic
potential energy. Similarly, when like poles move apart, they release magnetic
potential energy.) Rotating the compass so that its south end is closest to the
isolated north pole releases magnetic potential energy. Since objects always
accelerate so as to reduce their total potential energy as quickly as possible
and only magnetic potential energy is important here, the compass will rotate
so as to bring its south pole as close as possible to the isolated north pole.
Why: Like everything else, the compass accelerates so as to reduce
its total potential energy as quickly as possible. In this case, it turns to
bring its south pole close to the isolated north pole. Work is done during this
rotation and magnetic potential energy is released.
6. In reality, the situation described in Question 5 can never occur. Why not?
Answer: Isolated magnetic poles aren't found in nature
(equivalently, objects always have zero net charge or north poles are always
accompanied by equally strong south poles).
Why: There simply are no known fundamental particles that carry
magnetic poles. Without any basic north or south monopoles around, it's not
possible to make an accumulation of isolated north pole.
7. You continue along on your walk and come upon someone with another compass identical to yours. The two of you hold your compasses side by side and soon the white end of one compass is pointing toward the red end of the other compass. Each compass has a pair of equal but opposite poles and a net magnetic pole of zero, so why don’t all the forces between the two compasses cancel one another?
Answer: The strength of the force between two poles varies with
the distance separating them.
Why: When the red end of one compass is close to the white end of
the other compass, the attractive forces between those two opposite poles are
extremely strong. That's because they are so close. While there are also 3
other pairs of forces between the various pairs of poles on the two compasses,
those pairs are much farther apart and the forces are weaker.
8. Finally, you come to a sculpture that’s spun by the wind. The sculpture includes a rapidly turning aluminum wheel and you hold your compass up to that wheel. The wheel’s surface is directly north of you, so the red end of the compass needle starts out pointing toward that moving surface. But while aluminum metal is normally nonmagnetic, the moving aluminum somehow begins to twist the needle away from due north. The compass needle appears to be following the moving aluminum as though the aluminum were somehow pushing or dragging the needle along with it. Why does this effect occur?
Answer: The compass needle's magnetic field induces currents in
the moving aluminum and the aluminum becomes magnetic. The induced magnetism in
the aluminum exerts a magnetic drag force on the compass needle and drags its closest
pole along with the moving aluminum.
Why: Whenever a metal moves past a magnetic pole or the pole moves past the metal, an electric field acts to push current through the metal and the metal becomes magnetic. In the present case, the moving aluminum develops magnetic poles that push the closest pole of the compass needle away from the surface and also (somewhat surprisingly) drag the needle along in the direction of the moving aluminum. The reason for the magnetic drag force is that the repulsive poles forming in the aluminum are stronger on the side of the aluminum that is approaching the needle than they are on the side of the aluminum that is leaving the needle. Although the needle is repelled by both regions of the aluminum, the net force on the needle is away from the aluminum and also slightly in the direction that aluminum is moving. The reason for the difference in pole strength in the aluminum is that the poles in the aluminum moving toward the needle are freshest and haven't lost energy through heating of the aluminum metal. The poles in the aluminum moving away from the needle are old and have already converted some of their energy into thermal energy.