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<strong>Cosmic</strong> <strong>Game</strong> © Douglass A. White, 2012 v151207 218<br />

Benson, University Physics, p. 456, to show the electrical force on a single electron<br />

under these conditions:<br />

FE = eE = (1.6e-19 C) (100 N / C) = 1.6e-17 N. (directed upward)<br />

On the other hand, the gravitational force on the electron is:<br />

Fg = mg = (9.1e-31 kg) (9.8 N / kg) = 8.9e-30 N. (directed downward)<br />

In this example eE is the same as h f E / V in the <strong>com</strong>bination equation that we made<br />

above, but here we are just using the charge of a single electron for h f / V. Benson's<br />

example is to show how the electric force is much stronger than the gravitational force, so<br />

an electron can zip about in the sky and is significantly influenced only by<br />

electromagnetic forces in the environment. Thus we find that the effect of sunlight on<br />

the earth more than counteracts the effect of gravity in the case of subatomic particles.<br />

<strong>The</strong> textbook uses an example that leads the student away from noticing the possibilities<br />

of macroscopic photoelectric effects. Just before this example (on p. 450) Benson<br />

<strong>com</strong>putes the ratio of the gravitational force (Fg) to the electrostatic force (Fe) in terms<br />

of the interaction of two charged particles (an electron and a proton) to show how the two<br />

forces are separated by nearly 40 degrees of magnitude. Looked at one way, the two<br />

forces seem unrelated. Looked at another way, it should be a snap on our scale to use<br />

the electrical force to lift things beyond the influence of gravity. So why don't we do it?<br />

Our photoelectric formula contains E = h f as the energy of the light. For sunlight let's<br />

say the average frequency is about 1 PHz (10 15 Hz), going up to 30 PHz if we include<br />

ultraviolet frequencies. <strong>The</strong> energy is thus about in the range of 10 -17 J or 10 -18 J for a<br />

single photon to whack a single electron loose. We do not want to just move electrons,<br />

we want to lift payload.<br />

However, suppose we have a craft that has an effective photoelectric area of 9 square<br />

meters and the average insolation (solar power) per square meter is 250 W. <strong>The</strong> watt is a<br />

joule per second (W = J / s). That gives us about 2250 joules per second on the 9 m²<br />

surface.<br />

Let's calculate for a payload of 10 3 kg. <strong>The</strong> formula is h f E / V = m g.<br />

<strong>The</strong> fair weather field is about E = 10 2 N / C. We will solve for V.<br />

(2250 J / s) (10 2 N / C) / (10 3 kg) (9.8 m / s 2 ) = (23 J / C s) = 23 V / s.<br />

<strong>The</strong>n we rearrange to solve for the payload.<br />

(10 3 kg) = (2250 J) (10 2 N / C) / (23 V) (9.8 m / s 2 ).

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