Physics 106 - How Things Work – Spring, 2001

Problem Set #4 – Electrodynamics

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?

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.)

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?

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?

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.

6. In reality, the situation described in Question 5 can never occur. Why not?

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?

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?