6.2.3.P4
In the figure at the right are shown two settings of positive and negative charges (labeled I and II). Setting I has two positive charges; setting II has one negative charge and one positive charge. Each of the charges has the same magnitude, Q.
(i) If one large grid box in the diagram has a magnitude d, using E_{0} = k_{c}Q^{2}/d, express the total electric potential energy of each arrangement as
E = nE_{0}
where n is some dimensionless number.


(ii) In each setting, two positions are labeled. If a positive test charge of magnitude Q is added at each position (there is one test charge in the system at any time), rank the magnitude of the extra potential energy the charge would add to the system at each of the four places, indicating if any are 0. (Like this E=F>G>H=0).
Explain your reasoning.
(iii) There are two situations (I and II), two possibilities for the test charge (positive and negative), and four possible positions (A, B, C, and D). This gives 2 x 2 x 4 = 16 possibilities. Which has the largest electric PE? The largest magnitude of PE? The smallest PE?
Explain your reasoning.
Joe Redish 11/20/16
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