We consider a polymer brush grafted to a surface (acting as an electrode) and bearing a charged group at its free end. Using a second distant electrode, the brush is subject to a constant electric field. Based on a coarse-grained continuum model, we calculate the average brush height and find that the brush can stretch or compress depending on the applied field and charge end-group. We further look at an undulation mode of the flat polymer brush and find that the electrostatic energy scales linearly with the undulation wave number, q. Competition with surface tension, scaling as q2, tends to stabilize a lateral q-mode of the polymer brush with a well-defined wave length. This wavelength depends on the brush height, surface separation, and several system parameters.