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Electrodes and voltage
For ideal parallel plates E = V / d, C = eps0 eps_r A / d, U = C V^2 / 2 and the plates attract with F = eps0 eps_r A E^2 / 2. Real air breaks down near 3 MV/m, far above these fields.
Model checks
The science
What is modelled
Two large flat electrodes held at a voltage V, a distance d apart. In the ideal limit the field between them is uniform and the plates behave as a capacitor that stores energy in the field.
Equations
E = V / d,C = eps0 eps_r A / d,Q = C V.- Stored energy
U = C V^2 / 2 = Q V / 2 = Q^2 / 2C. - Force between the plates
F = eps0 eps_r A E^2 / 2 = U / dat constant voltage, equal to(V^2 / 2)|dC/dd|.
Checks run in the page
- Field from voltage and gap.
- Capacitance from permittivity and geometry.
- Three equivalent energy expressions.
- Force against a numerical derivative of C.
Honest simplifications
Ideal parallel plates: no fringe field, no edge enhancement, no space charge, no corona and no real breakdown physics (the 3 MV/m figure is the textbook uniform-field level for air at atmospheric pressure, and rough surfaces or large gaps break down at lower fields). Illustrative numbers only; never a basis for real high-voltage work.
What to try
- Press Short gap, high voltage and compare the field with the breakdown level.
- Press Dielectric sheet: capacitance, energy and force all scale with the relative permittivity.
- Halve the gap: the field doubles, the capacitance doubles and the force quadruples.