Answer
See answers.
Work Step by Step
Use Equation 17–8 for the capacitance, $C=\epsilon_o\frac{A}{d}$ . Here, the separation d between the plates is halved, therefore the capacitance doubles.
Use Equation 17–10 for the energy, $PE=\frac{Q^2}{2C}$ . Here, the charge Q stays constant and the capacitance doubles, so the energy is halved, i.e., it changes by a factor of 0.5.
b. The plates, being oppositely charged, want to come together. The work done to move them together is negative. The work is the change in the stored PE.
$$W=\Delta PE=\frac{1}{2}PE_i-PE_i=-\frac{1}{2}PE_i $$
$$=-\frac{1}{2}\frac{Q^2}{2C} =-\frac{1}{4}\frac{Q^2}{\epsilon_o\frac{A}{d}} $$
$$W=-\frac{Q^2d}{4\epsilon_o A} $$
