# Electric field generated by voltage on a sheet

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1. Aug 15, 2015

### Archer Borz

Hi All,

I'm trying to calculate the electric field at a point above a sheet with the voltage V. The space above is filled with a dielectric with known bulk conductivity and relative permittivity. And the sheet is electrically isolated from the space. My major is not physics so thanks for your help and education!

2. Aug 16, 2015

### Orodruin

Staff Emeritus
This is an incomplete question. Electrical fields depend on differences in voltage and without knowing more, the question cannot be answered.

3. Aug 16, 2015

### Archer Borz

Thanks Orodrin.
I tried to simplify my problem. Sorry to make it unsolvable in the process! Here is more detail in an example.
There is a conductive sheet covered with nonconductive material. (Let's simplify the nonconductive material effects on this problem to the fact that there is no current between the sheet and its surrounding) This sheet is over some body part (i.e. a muscle) with the initial voltage of 0 volts at t0. There is square voltage pulse over the sheet for w seconds (for example w=100ms). So, the voltage over the sheet is V1 initially and then is V2 for w seconds and then goes back to V1.
In reality, switching between V1 volts and V2 volts takes some time. This witching speed helped me to find the right values for the bulk conductivity and relative permittivity which I found them here: (http://niremf.ifac.cnr.it/docs/DIELECTRIC/Report.html#Results).
Let's assume ground (earth) is parallel to the sheet and d meter away from it. The body is between the sheet with the voltage pulse and the ground and there is no gap between the body and the sheet. As far as I know, electric fields can be monopole or dipole, so I am guessing that it is not essential to define a secondary voltage source like a ground. But if is it necessary to have 2 voltages lets assume d=1m. My guess is that by "differences in voltage" you are referring to the voltage change in time not a secondary source of voltage.
Would this be enough to estimate the effect of this voltage pulse in the body and calculate electric field or induced voltage at a point inside the body? Please feel free to simplify the problem in any way if I made it too complex.

4. Aug 16, 2015

### DrZoidberg

How exactly the field and the current flowing through different points of the body change over time depends on several factors. e.g. Where you place the sheet, what size and shape it has. The shape of the body and also how well the body is grounded.
Once you apply a voltage to the sheet, a current will start flowing through the body. If the person is well grounded then that current may drop to zero within less than one ms. That also depends on how thick the layer of non conductive material is, as that affects the capacity between the sheet and the skin. Then there is also the capacity between the surface of the skin and the inside of the body. And of course the resistance of the skin. All in all it's a complex system and it's difficult to calculate that precisely.
What do you need this for anyway?

5. Aug 16, 2015

### Archer Borz

Thank you DrZoidberg.

I'm trying to design a medical device. Recently some devices like https://en.wikipedia.org/wiki/Alternating_electric_field_therapy came to market that are very promising in some new applications like fighting cancer cells with E-Fields. I'm simply trying to get an estimate the effects of electric field generated by a charged sheet attached (but electrically isolated) to the body to figure out the level of voltage and the possible shape of signals to make a rough prototype.

what I'm getting from your kind answer, is that if the body is grounded then it minimize the effect of such an applications. And also it is a good idea to use dipole e-fields to maximize its local effects.

I am ignoring many details (like the effect of the skin as you mentioned and the thickness of the isolator) at the moment, just to get an estimation for some values that I need in order to start designing an adjustable prototype. Certainly in time I need to find a good simulator and body model to refine these values by simulation before trying it in vivo, but at the moment I am just trying to learn how I can calculate a reasonable estimation based on parameters that I can control and information that I can collect about human body's electrical characteristics. I'm trying to figure out the physics behind this problem in a very simplified model and educate myself a bit about its basics before taking a shortcut by using EMF simulators.

That is why I am simplifying the problem and ignoring almost all the details to just a big piece of muscle on top of a sheet connected to a voltage pulse.