Does the magnitude of an electrical field change with frequency? I am trying to model the frequency response of a force (dielectrophoresis) that is based on gradient of an electric field.
One of the components is the CM factor which has a frequency component, but the other factor is $\Delta E^2 $ 
I was wondering if this is affected by frequency? If the magnitude is $20\: \mathrm{v/m}$ at DC is it the same in AC conditions. 
If not, how does it change with frequency?
 A: The magnitude does not change with frequency, because the formula for an even wave is
$$
\Psi(x) = A\cdot e^{i(kx - \omega t)}  
$$
Where $A$ is the amplitude and $\omega$ is the frequency. So, if you change the frequency, the amplitude does not change.
A: Electric field is associated with any electrical signal or electromagnetic process. A plane wave carries no information, and is normally modulated (Amplitude modulation, phase modulation etc.) with respect to time, and any modulation means a frequency dependent amplitude, which will in turn mean a frequency dependent force.
I hope, this answer goes in the right direction.
A: Electromagnetic fields can be composed of a spectrum, not just a single frequency/wavenumber relation.  If there is a spectrum for the electric field in question (and yes, spectra can include the quasi-static or DC parts as well), then there is a frequency dependence in the amplitude.  Even in the case of the plane wave mentioned above, there is technically a frequency dependence.  Mathematically, $A$ is not explicitly defined as a function of $\omega$ or $k$.  However, if one calculated the FFT of such a signal, it would show a single peak at the corresponding $\omega$ or $k$.
In more complicated situations (i.e., nonlinear waves), then $A$ can equal $A(\omega, k)$.  Meaning, a generalized nonlinear signal can have both temporal and spatial dependencies in the amplitude and both $\omega$ and $k$ need not be purely real functions.
So if this is an experiment, then either produce the FFT or hook up the signal to a oscilloscope to determine the spectrum of the electric field.  The gradient operator will only affect/act-on $k$, but if $k$ is coupled to $\omega$ (e.g., through a dispersion relation), then the frequency dependence could still play a role.  If this is theory, then it is an issue of whether you want to approximate with linear theory or try nonlinear generalizations.
