Summary

We've now seen how the surface charges and electric fields perform a feedback loop:

1.

The charges (initially on the battery or capacitor) create an electric field in and around the circuit

2.

The electric field moves charges around the circuit, leaving excess charges on the surfaces of wires and at the junctions between wires with different resistivities

3.

Go to 1.

This process continues until the surface charges create an electric field through the wire that produces constant current throughout the circuit. This process is very fast, just a few light-crossing times, and so we normally don't notice this important sequence of events.

The student, armed with this knowledge, is now in a good position to answer the questions posed earlier:

• The battery doesn't ``know'' how much current to send to the circuit; the electric field of surface charges on the battery starts charges moving throughout the circuit, and the feedback process quickly equilibrates the circuit to constant-current conditions.
• The light bulb doesn't change brightness as the bulb is moved around, for the surface charges on the wires very quickly adjust to maintain constant current throughout the circuit.
• A resistor-capacitor circuit discharges for an important reason: the capacitor is finite in size, not the simpler infinite one usually studied. The fringe-field of the finite capacitor plates is important, for this is what will push charge around the circuit.

Current desktop computers are now powerful enough to calculate the surface charges on simple resistor-capacitor circuits (although not nearly fast enough for real-time visualization), and I have presented several examples. These show the same features as Chabay and Sherwood show in their text, but with additional details and effect. The relaxation calculations are not the true time-response of the circuit, but do help separate out various effects in these simple, but complicated, systems.

Other steps in the calculation, and visualizations of the electric potential for these circuits, are available from http://galaxy.cofc.edu/circuits.html.