Physics
Physics
Problem
A capacitor is connected across a constant battery. (a) Find the energy stored in the capacitor with air between the plates. (b) Without disconnecting the battery, a dielectric slab of dielectric constant is fully inserted between the plates so that the capacitance becomes four times its original value. Find the new energy stored in the capacitor. (c) Calculate the work done by the external circuit (battery) during the insertion of the dielectric and state in which form the additional energy supplied by the battery finally appears.Intuitive explanation
The key insight is that capacitance and stored energy depend on the dielectric material, but the battery maintains constant voltage throughout. When you insert a dielectric while the battery stays connected, the capacitance jumps up, which means more charge flows onto the plates—and the battery does work to push that extra charge. The energy supplied by the battery doesn't all stay in the capacitor; some goes into the mechanical work of pulling the dielectric in (or pushing it out, depending on the force direction).
Intuitive explanation
The key insight is that capacitance and stored energy depend on the dielectric material, but the battery maintains constant voltage throughout. When you insert a dielectric while the battery stays connected, the capacitance jumps up, which means more charge flows onto the plates—and the battery does work to push that extra charge. The energy supplied by the battery doesn't all stay in the capacitor; some goes into the mechanical work of pulling the dielectric in (or pushing it out, depending on the force direction).