Explanation

(a) Work is required to set up the four charge configuration
$q_{1} = + q,\ q_{2} = - q,\ q_{3} = + q\ \ and\ q_{4} = - q$
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$W = \frac{1}{4\pi\varepsilon_{0}}\left\lbrack \frac{( + q)( - q)}{AB} + \frac{( - q)( + q)}{BC} + \frac{( + q)( - q)}{CD} + \frac{( - q)( + q)}{DA} + \frac{( + q)( + q)}{AC} + \frac{( - q)( - q)}{BD} \right\rbrack$
$W = \frac{1}{4\pi\varepsilon_{0}}\left\lbrack - \frac{q^{2}}{a} - \frac{q^{2}}{a} - \frac{q^{2}}{a} - \frac{q^{2}}{a} + \frac{q^{2}}{a\sqrt{2}} + \frac{q^{2}}{a\sqrt{2}} \right\rbrack$
$W = \frac{1}{4\pi\varepsilon_{0}}\frac{q^{2}}{a}\left\lbrack - 4 + \sqrt{2} \right\rbrack = \frac{1}{4\pi\varepsilon_{0}}\frac{q^{2}}{a}\lbrack - 4 + 1.414\rbrack$
$W = - 0.21 \times \frac{q^{2}}{\varepsilon_{0}a}\ \ \ \ \ \ \ \ (approx.)$