Dielectrics
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.
Filling the gap with an insulator (a dielectric) multiplies the capacitance by its dielectric constant: C = κC0. The dielectric’s molecules polarize and partly cancel the field. What else changes depends on whether the battery is still connected.
1. Why it works
2. Partly filled capacitors
Side by side (dielectric fills part of the area, full gap): the two parts share the same ΔV, so they’re in parallel: add capacitances.
Layered (dielectric fills part of the gap, full area): the same charge passes through each layer, so they’re in series: add reciprocals.
Isolated capacitor: sliding in a dielectric lowers the energy, so the capacitor actually pulls the slab in.
With a battery connected, the battery supplies extra charge and the stored energy goes up by κ.
3. Example, then try it
A 10 pF air capacitor is filled with a dielectric of κ = 3.0. Find its new capacitance. If it was isolated with 50 V across it, what is the new voltage?
C = (3.0)(10) = 30 pF.
Isolated, Q is fixed, so ΔV = 50 ÷ 3.0 ≈ 17 V.
An air-filled parallel-plate capacitor has C0 = 40 pF. A slab with κ = 4.0 is inserted in two ways: (a) filling the left half of the area, full gap; (b) filling the bottom half of the gap, full area. Find C each way.
(a) Side by side → parallel: each half-area part is C0/2 = 20 pF of air; the filled half becomes κ(20) = 80 pF.
(a) Total: 20 + 80 = 100 pF (2.5C0).
(b) Layered → series: each half-gap layer alone is 2C0 = 80 pF of air; the dielectric layer becomes κ(80) = 320 pF.
(b) Total: 1/C = 1/80 + 1/320 = 5/320, so C = 64 pF (1.6C0).
Answer: (a) 100 pF; (b) 64 pF.
4. Common mistakes
A dielectric with constant κ is slid into an isolated, charged capacitor. What happens to the electric field between the plates?
Q is fixed, and the polarized dielectric partly cancels the plates’ field: E = E₀/κ, and so ΔV = Ed drops by κ too.
Ready to practice?
5 questions on Dielectrics, each with a hint and an explanation for every wrong answer.