On the Electric Polarization of Current Bearing Wires/Resistors
Fig. 1 depicts an open circuit, consisting of a battery and a resistive wire. The battery terminals are the sources of a conservative E field. Negative conduction electrons have automatically accumulated such that E=0 at all points within the wire. (This rearrangement of negative charge engenders a net positive charge at points closer to the negative terminal.)
An Open Circuit
If the circuit in Fig. 1 is closed, conduction electrons flow from the battery’s negative terminal into the wire, and from the wire into the battery’s positive terminal. Since E=0 at all points in the wire at the instant the switch is closed, it might be wondered what the physical basis for this current is.
One suggested mechanism is as follows. The original excess positive charges near the battery’s negative terminal induce negative charges to flow into the wire from the negative terminal. This quickly neutralizes the excess positive charge. Furthermore, because of the wire’s resistance, there is actually a pile up of negative charges near the negative terminal. Such a charge reversal pushes conduction electrons, further out in the wire, along toward the positive terminal. In a short time the wire acquires a net negative charge density at points closer to the negative terminal.
When the switch is closed, negative charge flow also occurs near the battery’s positive terminal. In this case conduction electrons flow from the wire into the battery’s positive terminal. In a short time the wire acquires a net positive charge density at points closer to the positive terminal. Although the wire’s net charge theoretically remains zero after a steady current has been established, closing the switch has quickly resulted in a reversal of the wire’s electric polarity and a nonzero E at points within the wire.
Quite as they did with the switch open, conduction charges move in such a manner as to try to drive E to zero at internal points. However, negative charge can no longer pile up close to the positive terminal, and the current continues unabated.
Ohm’s Law specifies the magnitude of the current: I=V/R. A plausible, classical model for this formula can be found in The Berkeley Physics Series, V2, by the late E.M.Purcell. For present purposes, the interesting idea is that a static, nonzero charge density can theoretically be expected around the circuit once a steady current has been established. On the negative terminal end of the wire this charge density will be negative, and it will taper off to zero at the circuit’s "midpoint." The density will then be become positive, and its magnitude will increase as one moves further along toward the positive terminal.
The maximum charge density magnitudes, at the two battery terminals, will be a function of the wire’s resistance: The greater the resistance, the greater the maximum charge density magnitudes.
Fig. 2 depicts a method for testing this model. There are now three switches, one at each terminal and one at the wire’s midpoint. Originally all three switches are closed and a steady current flows. Each switch can be triggered open by a light pulse from a centrally located source.
Simultaneously Opening Switches
The three switches are simultaneously opened, and the left and right halves of the wire are straightened and far removed from the battery. They are arranged as shown in Fig. 3, and tested for a potential difference. If the varying charge density model is correct, a potential difference should be observed.
Testing for Wire Electric Polarization