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The energy stored by any pair of positive charges is inversely proportional to the distance between them, and directly proportional to their charges. Three identical point charges start at the vertices of an equilateral triangle, and this configuration stores 15 Joules of energy. How much more energy, in Joules, would be stored if one of these charges was moved to the midpoint of the opposite side?

 Jan 11, 2019
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\(\text{You start with a configuration of 3 charges separated by a distance }s\\ \text{By symmetry each pair of charges generates the same energy and thus }\\ \text{each configuration generates }\dfrac{15}{3} = 5J\\ \text{Now we move the charge to the midpoint between two other charges}\\ \text{Our new configuration is one pair separated by distance }s\\ \text{and 2 other pairs separated by distance }\dfrac s 2\)

\(\text{The pair separated by }s \text{ generates }5J \text{ as before}\\ \text{The energy stored is inversely proportional to the distance between them}\\ \text{so halving the distance doubles the energy}\\ \text{thus we have two pairs that generate }2 \cdot 5J = 10J \text{ each}\\ \text{Totaling these up we have } E = (5+10+10) = 25J\)

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 Jan 11, 2019

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