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Floating Potential Condition

The floating potential condition imposes a constraint on the electric potential \(\phi\), requiring that its value in a given region be constant:

\[ \left. \phi \right|_{\Omega} = \mathrm{const}, \]

where \(\Omega\) is the given region of space. This condition is used when a region must be held at a constant (but a priori unknown) electric potential while remaining in contact with surrounding regions where \(\phi\) is determined by the field equation.

When to use this

  • Isolated metal conductors (intermediate electrodes, guard rings) that are not connected to a voltage source — the conductor's equipotential value is part of the solution.
  • Capacitance-matrix extraction — drive one electrode and let the others float to compute self / mutual capacitances.
  • Floating gates in MEMS / semiconductor structures.
  • Lightning-protection studies of ungrounded metallic appendages.

Usage

from mufem.electromagnetics.electrostatics import FloatingPotentialCondition

floating_bc = FloatingPotentialCondition(
    name="Floating Electrode",
    marker="MiddleConductor" @ Vol,
)

electrostatics_model.add_condition(floating_bc)