Simple Nature - Light and Matter

Constant voltage means that no work would be done on a chargeas it moved from one point in the conductor to another. If zero workwas done only along a certain path between two specific points, itmight mean that positive work was done along part of the path andnegative work along the rest, resulting in a cancellation. But there isno way that the work could come out to be zero for all possible pathsunless the electrical force on a charge was in fact zero at every point.Suppose, for example, that you build up a static charge by scuffingyour feet on a carpet, and then you deposit some of that charge ontoa doorknob, which is a good conductor. How can all that charge bein the doorknob without creating any electrical force at any pointinside it? The only possible answer is that the charge moves arounduntil it has spread itself into just the right configuration so that theforces exerted by all the little bits of excess surface charge on anycharged particle within the doorknob exactly cancel out.We can explain this behavior if we assume that the charge placedon the doorknob eventually settles down into a stable equilibrium.Since the doorknob is a conductor, the charge is free to move throughit. If it was free to move and any part of it did experience a nonzerototal force from the rest of the charge, then it would move, and wewould not have an equilibrium.Excess charge placed on a conductor, once it reaches its equilibriumconfiguration, is entirely on the surface, not on the interior.This should be intuitively reasonable in figure h, for example, sincethe charges are all repelling each other. A proof is given in example35 on p. 623.Since wires are good conductors, constancy of voltage throughouta conductor provides a convenient freedom in hooking up avoltmeter to a circuit. In figure i, points B and C are on the samepiece of conducting wire, so V B = V C . Measuring V B − V A gives thesame result as measuring V C − V A .h / 1. The finger deposits chargeson the solid, spherical, metaldoorknob and is then withdrawn.2. Almost instantaneously, thecharges’ mutual repulsion makesthem redistribute themselves uniformlyon the surface of thesphere. The only excess chargeis on the surface; charges do existin the atoms that form the interiorof the sphere, but they arebalanced. Charges on the interiorfeel zero total electrical force fromthe ones at the surface. Chargesat the surface experience a netoutward repulsion, but this is canceledout by the force that keepthem from escaping into the air.3. A voltmeter shows zero differencein voltage between anytwo points on the interior or surfaceof the sphere. If the voltagedifference wasn’t zero, thenenergy could be released by theflow of charge from one point tothe other; this only happens beforeequilibrium is reached.i / The voltmeter doesn’t carewhich of these setups you use.Section 9.1 Current and Voltage 523