Physic Labs

Electricity and magnetism

Capacitors and capacitance

Explore a parallel-plate capacitor: measure the field between plates as area, gap, and voltage vary. Verify C=ε0A/dC = \varepsilon_0 A/d, Q=CUQ = CU, and stored energy W=12CU2W = \frac{1}{2}CU^2.

High school

⚠ This simulation uses low voltage; real capacitors can hold dangerous charge even after power is removed — always discharge through a resistor before touching.

Equipment

  • Virtual parallel-plate capacitor and voltage source
  • Sliders for plate area, plate gap, and voltage
  • Field and energy readouts

Procedure

  1. Measure field vs voltage and gap

    Keep "Plate area" fixed; raise "Voltage" and read the field — check E=U/dE = U/d. Then hold U constant, increase "Plate gap", and watch EE fall inversely with dd. Record three (U, d, E) triples.

  2. Verify the capacitance formula

    Vary "Plate area" and "Plate gap" to see capacitance follow C=ε0A/dC = \varepsilon_0 A/d: doubling A doubles C; doubling d halves it. Watch charge Q=CUQ = CU accumulate on the plates in figure 1 (charge density shown on both plates).

  3. Compute the stored energy

    At two different voltages, read the energy and check W=12CU2=Q22CW = \frac{1}{2}CU^2 = \frac{Q^2}{2C}: doubling U quadruples W. Predict what happens if a dielectric εr>1\varepsilon_r > 1 fills the gap (C rises by εr\varepsilon_r) — connecting to the dielectrics section.

Simulation

Experiment history

The first capacitor was the Leyden jar, built independently in 1745–46 by Ewald Georg von Kleist and Pieter van Musschenbroek at Leiden — a glass jar lined inside and out with metal that stored startling amounts of charge. Benjamin Franklin showed the charge resides in the glass, not the water, and laid groundwork for the positive/negative charge convention. In 1837 Michael Faraday showed that a dielectric between the plates increases charge storage — the ratio is now called the dielectric constant; the farad unit bears his name. Maxwell then placed the capacitor into his field equations through the displacement current ∂D/∂t\partial \mathbf{D}/\partial t — the link that allows electromagnetic waves to exist.

Related physicists

James Clerk MaxwellMichael Faraday

Related library topics

Capacitors and capacitance