AP® Physics 2: Algebra-Based · Unit 10 · Topic 10.6
Dielectrics and Stored Energy
A dielectric is an insulator slipped between capacitor plates that weakens the field and lets the plates hold more charge at the same voltage. The energy stored in any capacitor is U = 1/2 C V2, not QV, because voltage builds up gradually as charge arrives.
Charge two parallel plates and an electric field forms between them, pointing from positive to negative. Slide an insulating slab, a dielectric, into that gap and its molecules respond. Either they already have a slight separation of positive and negative charge, or the field induces one, and these molecular dipoles twist to line up against the field. The slab develops a thin layer of negative charge facing the positive plate and positive charge facing the negative plate. That layer creates its own field pointing backward, partially canceling the field from the plates. With a weaker net field, the same amount of charge on the plates produces a lower voltage, which means the capacitor's capacitance C = Q/V has gone up. A bigger C lets the capacitor store more charge for the same voltage, or the same charge at a lower voltage, either way packing in more.
Energy enters the picture because charging a capacitor is work. A battery does not dump charge onto the plates against a fixed voltage. The voltage starts at 0 and climbs to its final value V as charge Q piles up, so the average voltage during the whole process is V/2. That is why stored energy is U = 1/2 QV, which combines with Q = CV to give U = 1/2 C V2, the version used for calculations.
This connects directly to what comes before and after in the unit. Capacitance itself, C = Q/V, sets the stage, and dielectrics are simply a way to raise C by weakening the field for a given charge. If a battery stays connected while a dielectric is inserted, V is fixed, C rises, so Q = CV rises and U = 1/2 C V2 rises too, since the battery keeps supplying more charge.
Key terms
- Dielectric
- An insulating material placed between capacitor plates that reduces the net electric field and increases capacitance.
- Capacitance
- The ratio C = Q/V, measuring how much charge a capacitor stores per volt across it.
- Induced dipole
- A temporary separation of positive and negative charge within a molecule caused by an external electric field.
- Stored energy
- The work needed to charge a capacitor, given by U = 1/2 C V2 or equivalently 1/2 Q V.
Watch it explained
- How it worksHow do the molecules in a dielectric line up and cancel part of the field between the plates?
- Worked exampleFind the energy stored in a 20 microfarad capacitor charged to 12 V.
- Common mistakeWhy isn't the energy stored in a capacitor equal to charge times voltage?
- Going furtherWhat happens to the stored energy when a dielectric is pushed in while the battery stays attached?
Check yourself
End of topic.