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The $\nu=\frac{5}{2}$ fractional quantum Hall effect is of experimental andtheoretical interest due to the possible non-Abelian statistics of theexcitations in the electron liquid. A small voltage difference across a sampleapplied in experiments to probe the system is often ignored in theoreticalstudies due to the Galilean invariance in the thermodynamic limit. Noexperimental sample, however, is Galilean invariant. In this work, we explorethe effects of the probe electric fields in a disk geometry with finitethickness. We find that weak probe fields enhance the Moore-Read Pfaffian statebut sufficiently strong electric fields destroy the incompressible state. In adisk geometry, the behavior of the system depends on the polarity of theapplied radial field, which can potentially be observed in experiments using ina Corbino disk configuration. Our simulation also shows that the application ofsuch a field enhances the coherence length of quasiholes propagating throughthe edge channels

In-plane electric fields and the $\nu=\frac{5}{2}$ fractional quantum Hall effect in a disk geometry