Page:Electricity (1912) Kapp.djvu/69

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 $A$.