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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?

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Force on what? Can you clarify your question with a picture of some sort or maybe a more descriptive problem setup? – BMS Dec 4 '13 at 21:02
When you talk about magnitude of a DC current, it is well understood. But for AC, you have to clarify if it is peak to peak or rms value. Either way, it would not depend on frequency at all. – mcodesmart Dec 4 '13 at 21:40
Related (duplicate?) :… – jinawee Dec 4 '13 at 22:01

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.

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For LaTeX you surround the block with $$ \\LaTeX Lines $$ or $LaTeX Inline$ for inline. I also submitted an edit for your post to fix that. As far as the question, would the field not change because in AC the charge movement change would produce a change in the electromagnetic field, and this change would depend on the frequency of the current? – danielu13 Dec 4 '13 at 21:10
@danielu13: Thank you for the help! Can you rewrite your answer a bit? I do not understand completely what you mean... – arc_lupus Dec 4 '13 at 21:13
This makes sense for just the electric field, but what about the gradient of an Electric field? $\delta E / \delta x $ – user35262 Dec 4 '13 at 23:06
Correction to my deleted comment: The absolut value of the gradient becomes bigger everywhere except for the maxima and minima when you increase the frequency. – arc_lupus Dec 5 '13 at 6:30

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.

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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.

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Thanks for fixing the Tex characters @KyleKanos, I just realized that the comments accepted Tex syntax after I posted this comment. – honeste_vivere Sep 12 '14 at 14:34

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