Capacitance between ground and copper loop in the air

[LorDjidane]

Hello there

I'm currently working on an EM device that should be able to measure the humidity in the ground. I cannot give too many details, but let's consider the following issue:

I have a copper closed loop in which I send some current to generate a magnetic field. But there are some EM 'parasites', making my measurements unaccurate.

First of all, I'd like to compute the capacitance existing between my closed loop and the ground (note that the loop is at h=70cm height from the ground plus it has a diameter of 1m and a width of 3cm).

Here are my computations. I think I went way too fast, but this was only to get a rough idea in 30s about the expected value.

(s stands for sigma, e for epsilon, S for surface; I'm sorry, i will write down the latex stuff later)

Ground => E = s/2e
Loop => Q = I\Deltat (an approximation of my loop as a wire)

Then, Gauss theorem: E = Q/Se (that's the epsilon of the wire; I don't know what surface to take, i assume this is the surface seen by the ground?)

Total field: E = s/2e + I\Deltat/Se

Then I integer over the height h, since \DeltaU = -\int{E}, over h.

And that leaves me with:

C = Q/U (this Q is the total charge in the system (ground + loop))

C = [(s_ground/S_ground) + I\Deltat] / [h{(s_ground/2e_ground) + I\Deltat/(S_wire*e_wire)}]

(damn this is horrible; i'll correct it)

 

[LorDjidane]

With this very simple model, I obtain a capacitance value of 3pF. That seems correct, I will just have to correct it to get some more details (I expect the value to be more around 7-10 pF).

What do you think?