Final answer:
The energy stored in an isolated charged capacitor decreases when a dielectric is inserted, because the capacitance increases while the charge remains constant. Work is done during the insertion of the dielectric material.
Step-by-step explanation:
Energy Change in a Charged Capacitor with a Dielectric Inserted
When a dielectric is inserted into an isolated charged capacitor, the energy stored in the capacitor decreases. This is because the insertion of a dielectric increases the capacitance but the charge remains constant. The energy (U) stored in a capacitor is given by the equation U = Q^2/(2C), where Q is the charge and C is the capacitance. When a dielectric is introduced, the capacitance (C) increases, which results in a decrease in the energy (U) since the charge (Q) is constant in an isolated system. As for work being done, it is required to insert the dielectric into the gap between the plates of the capacitor, so the correct answer is b) Energy decreases; work was done.
It's important to note that if the capacitor were connected to a battery instead of being isolated, the potential difference across the plates would stay constant and the energy stored would increase because additional charge would be supplied by the battery to maintain the voltage. In the case of the isolated capacitor, the decrease in energy can be thought of as the energy required to polarize the dielectric medium.