Explanation

(a) Change in energy $\mathrm{\Delta}U = \frac{1}{2}\left\lbrack \frac{q_{1}^{2} - q_{2}^{2}\rbrack}{C} \right\rbrack$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{1}{2}\left\lbrack \frac{(0.5)^{2} - (0.1)^{2}}{48 \times 10^{- 6}} \right\rbrack$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{1}{2}\left\lbrack \frac{0.25 - 0.01}{48 \times 10^{- 6}} \right\rbrack$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{1}{2}\left\lbrack \frac{0.24}{48 \times 10^{- 6}} \right\rbrack = \frac{1}{2}\left\lbrack \frac{10^{4}}{2} \right\rbrack = 2500\ J$