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PRACTICE / Parallel-plate capacitors

Two plate areas share voltage, not charge

An isolated parallel-plate capacitor initially has capacitance 4 pF and voltage 100 V. A dielectric with κ = 3 fills the full gap over exactly half the plate area; the other half stays vacuum.

What is the final voltage?

Organize the givens & assumptions
  • Initial C = 4 pF
  • Initial V = 100 V
  • Half area has κ = 3
  • Battery disconnected

Ideal linear dielectric, fixed plate separation and area, negligible fringing, no charge leakage; the two regions span the same full plate gap.

  1. A50 V50\ \mathrm V
  2. B100 V100\ \mathrm V
  3. C1003 V\frac{100}{3}\ \mathrm V
  4. D2003 V\frac{200}{3}\ \mathrm V

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