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Let's say I have a circle filled with positive charges. Some distance away I have an identical circle filled with negative charges. Since the distribution is uniform in the circles, I can just use the center of the circles as points and calculate the field lines between the two. So far so good. Now let's say I connect the first circle to the second by a resistor. If the sum of the charges are so large that it is essentially unchanged for some length of time (as in I have constant charges and constant current), how can I calculate the electric field?