  A two-dimensional free boundary transmission problem arising in the modeling
of an electrostatically actuated plate is considered and a representation
formula for the derivative of the associated electrostatic energy with respect
to the deflection of the plate is derived. The latter paves the way for the
construction of energy minimizers and also provides the Euler-Lagrange equation
satisfied by these minimizers. A by-product is the monotonicity of the
electrostatic energy with respect to the deflection.
