The images below are visualizations of the electric charges and fields in a simple resistor-capacitor circuit with a complicated path. The resistor is a uniform copper wire joining the two plates. The different images represent computational steps in the evolution of the circuit.
The wires and plates are divided into computational cells, each a cube 0.5 mm on a side. The entire circuit is 25 mm (about one inches) across, the wires are 5 mm thick, and this image is a slice through the mid-plane of the circuit.
The time-step used in the calculations was 0.75 ps, which is about one-half the time for light to cross a computational cell. Light would take about 180 ps, or about 245 time steps, to cross the circuit.
The colors represent the amount of excess charge in each cell, from red (5000 or more positive elementary charges), to white (neutral), to blue (5000 or more negative elementary charges). The arrows show the magnitude and direction of the retarded electric field due to all the charges calculated at that point. (The very large electric fields present in and between the plates are not drawn so the much smaller fields in the wires are visible.)
Click on an image for a larger, clearer picture (615x795 pixels, about 50k each).
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(0 steps) |
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(58 steps = 43.5 ps) |
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(83 steps = 62 ps) |
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(120 steps = 90 ps) Electric fields are magnified 400% from the previous pictures to show the smaller fields away from the capacitor. |
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(150 steps = 112 ps) |
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(300 steps = 225 ps) |
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(400 steps = 300 ps) |
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(600 steps = 450 ps) |
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(900 steps = 675 ps) |
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(1800 steps = 1350 ps) |