AP® Physics C: Electricity and Magnetism · Unit 10 · Topic 10.4
Inserting a Dielectric, Isolated or Connected
Sliding a dielectric into a capacitor always raises C by a factor of kappa, but whether Q, V, or the stored energy changes depends on whether the capacitor is isolated or still hooked to a battery.
A dielectric is an insulator whose molecules polarize in an electric field. Slide one into the gap between the plates and it builds its own small internal field pointing backward against the field from the plates. That weakens the net field inside, which is why the capacitance C = kappa C0 goes up — the capacitor can now hold more charge per volt. Everything else follows from this one fact plus Q = CV.
If the capacitor is isolated, the charge Q on the plates has nowhere to go, so Q is locked. Since V = Q/C and C just grew, V must fall. Energy stored is U = Q2/(2C), and since Q is fixed while C grows, U drops: some energy left the field as the dielectric was pulled in, doing work on it. If instead the battery stays connected, the battery holds V fixed. Now Q = CV must rise to match the bigger C, and U = (1/2)CV2 rises too, because the battery pushes extra charge onto the plates to keep V constant, and that charge brings energy with it.
This is the same C = kappa C0 relationship from dielectric constants, just applied to two different constraints. It sets up energy density and force-on-dielectric problems next, where you track whether charge or voltage is the fixed quantity before trusting any energy formula.
Key terms
- Dielectric constant (kappa)
- A factor greater than 1 describing how much an insulator increases a capacitor's capacitance when it fills the gap.
- Isolated capacitor
- A capacitor disconnected from any circuit, so its charge Q cannot change once set.
- Capacitance
- The ratio C = Q/V, describing how much charge a capacitor stores per volt across it.
- Polarization
- The alignment of a dielectric's molecules in an external field, creating an internal field that opposes it.
Watch it explained
- How it worksWalk me through the difference between inserting a dielectric with the battery on and off.
- Worked exampleFind the new charge on a 5 microfarad capacitor at 10 volts when a kappa 3 slab goes in.
- Worked exampleFind the energy change when a kappa 2 slab slides into an isolated charged capacitor.
- Common mistakeWhy doesn't the stored energy always rise when a dielectric is pushed into a capacitor?
Check yourself
End of topic.