Four identical point charges (q = +13.0 µC) are located on the corners of a rect

Question

Four identical point charges (q = +13.0 µC) are located on the corners of a rectangle, as shown in the figure below. The dimensions of the rectangle are L = 55.0 cm and W = 12.0 cm. Calculate the change in electric potential energy of the system as the charge at the lower left corner in the figure is brought to this position from infinitely far away. Assume that the other three charges in the figure below remain fixed in position.

In J?

Four identical point charges (q = +13.0 C) are located on the corners of a rectangle, as shown in the figure below. The dimensions of the rectangle are L = 55.0 cm and W = 12.0 cm. Calculate the change in electric potential energy of the system as the charge at the lower left corner in the figure is brought to this position from infinitely far away. Assume that the other three charges in the figure below remain fixed in position.

Explanation / Answer

Initial potential energy = kq2(1/L + 1/W + 1/(W2 + L2)0.5)

Final potential energy = 2 kq2(1/L + 1/W + 1/(W2 + L2)0.5)

Change in potential energy = kq2(1/L + 1/W + 1/(W2 + L2)0.5)

change in P.E = 9(109)(13)2(10-12)(1/0.55 +1/0.12 + 1/(0.552 + 0.122)0.5)J

= (169)(9)(11.93)/1000 = 18.142J

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