Page:Electricity (1912) Kapp.djvu/69

Rh where $$V$$ is the potential in dyne-centimetres, $$Q$$ the charge on the sphere in electrostatic units, and $$D$$ the distance of the point from the centre of the sphere in centimetres at which the approaching motion has terminated.

The reader should note that the conception of a person actually carrying a body containing unit charge in his hand, and approaching it to the sphere, is merely introduced as illustrating a mathematical relation between certain quantities, and must in no ways be taken literally. The formula only says that the potential is an attribute of the particular point $$A$$ in space distant $$D$$ cm. from the centre of the active mass $$Q$$. In another point, $$A_1$$ distant $$D_1$$ cm., the potential will have a different value, say $$V_1$$ If $$A$$ is nearer to the active centre than $$A_1$$, then $$V$$ will be greater than $$V_1$$, and we may therefore speak of a potential difference $$V - V_1$$ existing between the points $$A$$ and $$A_1$$. Or in symbols

$$V - V_1 = Q \left( \frac{1}{D} - \frac{1}{D_1}\right)$$

Since $$D$$ is smaller than $$D_1$$, the potential difference is positive. We must expend energy in bringing the unit positive charge, and in fact any positive charge, from $$A_1$$ to $$A$$.