Displacement Current⚠ unverified
Physics / Electromagnetics · Compute the Maxwell displacement current from a changing electric field
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| dE | dE | V*m | 1.0 | Change |
| dt | dt | s | 1.0 | Time interval over which the field changes |
| epsilon | ε | F/m | 8.85e-12 | Permittivity of the medium, in farads per metre (F/m). Default is 8.85e-12 |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Id | A | Displacement current, in amperes (A). Returns 0.0 when ``dt`` is not positive |
The science & history
Understanding the Parameters
- $\Delta E/\Delta t$ — rate of change of electric field between capacitor plates (approx).
- $\varepsilon$ — free-space or dielectric permittivity.
- $I_d$ — continues the “current” through a capacitor in the Ampere–Maxwell law so that $\nabla\times\mathbf{B}$ sees $\mathbf{J} + \partial\mathbf{D}/\partial t$.
Derivation (Approaching a Proof)
In a charging capacitor, conduction current stops in the gap but $Q = \varepsilon A E$ on the plates changes: $I = dQ/dt = \varepsilon A\,dE/dt$. Maxwell identified $\varepsilon A\,dE/dt$ as displacement current equal to the conduction current in the wires. Continuity of total current closes the circuit in Ampere’s law.
History
James Clerk Maxwell introduced displacement current (1860s) to make Ampere’s law consistent with charge conservation and to predict electromagnetic waves.
Related Concepts: Parallel-Plate Capacitance, Induced Emf, Poynting Vector, Magnetic Field Wire
Notes: Registry calculator displacement-current (unverified). Simplified scalar form; confirm
whether area is unity in the implementation. Unit caveat: $\Delta E$ label may be wrong (V·m vs V/m).