Talk:Voltage

Being only a lay person, I find analogies a great help in understanding technical and scientific matters.

I would like an explanation of what is illustrated by different forms of the analogy of pysical topology: a slope and its steepness and length; a precipice and its height; in terms of flowing water, the volume of water in the flow? -- Janos Abel 16:59, 6 June 2007 (CDT)

Possible analogy

A potential is a scalar function whose gradiant (or directional derivative) is equal to a vector field (typically force). In the case of voltage, force is given by Coulomb's law

$F={\frac {Cq_{1}q_{2}}{r^{2}}}$

and in the case of gravitation, force is given by Newton's law

$F={\frac {Gm_{1}m_{2}}{r^{2}}}$

The two situations are analogous, except that charge can be positive or negative, but mass cannot. In either case, the potential is just the force per unit charge (or mass). When an electron and proton are moved apart, the attractive force goes down, but the distance increases. An easy thing to remember is that in the potential one charge disappears, and the potential difference is proportional to 1/r. Formally,

${\frac {d}{dr}}\left({\frac {1}{r}}\right)=-{\frac {1}{r^{2}}}$

Now, back to the analogy: the potential depends on the height, but is independent of the mass because it measures the gravitational attraction the earth exerts per unit mass. Greg Woodhouse 17:48, 6 June 2007 (CDT)