Electric potential energy:

$\overline{){\mathbf{U}}{\mathbf{=}}\frac{\mathbf{k}{\mathbf{q}}_{\mathbf{1}}{\mathbf{q}}_{\mathbf{2}}}{\mathbf{r}}}$

When the charge 2q is far away, the system potential is contributed by 3 charges.

r_{q,-3q} = d

r_{5q,-3q} = d

r_{q,5q} = (d^{2} + d^{2})^{(1/2)} = 2^{(1/2)}d

Four point charges form a square with sides of length d, as shown in the figure. In the questions that follow, use the constant k in place of .

What will be the potential energy U_{tot }of the system of charges when charge +2_{q} is at a very large distance from the other charges?

Express your answer in terms of q, d, and appropriate constants.

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