Simple RC Circuit with Sinuous Wire

The images below are visualizations of the electric charges and fields in a simple resistor-capacitor circuit. In this circuit, all the wires have the same resistivity, but the extra bends in the wire result in a more complex arrangement of surface charges. The different images represent computational steps in the relaxation solution of the circuit.

The wires and plates divided into computational cells, each a cube 0.25 mm on a side. The entire circuit is 25 mm (about an inch) across, the wires are 5 mm thick, and this image is a slice through the mid-plane of the circuit.

The colors represent the amount of excess charge in each cell, from red (1000 or more positive elementary charges), to white (neutral), to blue (1000 or more negative elementary charges). The arrows show the magnitude and direction of the electric field (due to all the charges) calculated at that point.

Click on an image for a larger, clearer picture (800x600 pixels, about 25k each).

	This shows the capacitor at t=0, when charges are placed on the inner surfaces of the left- and right-hand plates. The white color indicates no excess charges are present elsewhere in the circuit. The field vectors are very large near the plates, and elsewhere look like the field of an electric dipole. Especially note the direction of the electric field in the highlighted area: the current will ultimately flow in the opposite direction to this dipole field. The reversed electric field must be created not only by the charges on the capacitor, but by surface charges throughout the circuit.
	(5 steps) We see polarization effects on the inner surfaces of the wire, but the electric fields are hardly changed yet. The arrowheads have been removed from the vectors for clarity; they are present on the larger images.
	(10 steps)
	(20 steps)
	(40 steps)
	(80 steps) Note the electric field in the indicated region has now reversed direction! Charges can finally start flowing from the positive plate to the negative plate, although not equally in all parts of the circuit (yet).
	(160 steps)
	The last frame (300 steps) The circuit has slowly relaxed to steady-state, in which the same current flows in all parts of the circuit.

Norris Preyer