Page:Electricity (1912) Kapp.djvu/28

24 cost and have overcome all the technical difficulties. Let us first, without altering the amount of charge on each sphere, merely shift their positions so as to get different distances. Measuring the force in each case, we will find that this force varies inversely as the square of the distance. We have thus verified part of our general equation. Now let us retain one particular distance and change the amount of charge, first on one sphere only and then on both. We find that the force varies directly as the product of the two charges. This experiment confirms the rest of the equation.

Writing now $$Q$$ and $$q$$ for the quantity of charge on each sphere the general equation takes the form

$$F = f \frac{Qq}{D^2}$$

In the case of both spheres containing equal charges this may also be written as an equation between the product of $$F$$ and $$D^2$$ on the one hand, and $$f$$ and $$Q^2$$ on the other—

$$F \times D^2 = f \times Q^2$$

Suppose we have succeeded in so adjusting the charges that $$F \times D^2$$ is unity; this might be the case for $$D = 10 cm$$. and $$F = \frac{1}{100}$$ dyne,