Current density of specific configuration

[peroAlex]

Homework Statement

Two hollow metal spheres (left one has radius of 0.7 meters and right one has radius of 0.4 meters) are half-submerged in the sea water with specific conductance of γ = 4 S/m. Distance between their centers is much greater than their radii dimensions and equals 60 meters. Both spheres are connected with real voltage source (U = 300V and R = 4Ω).
Here's the sample image URL (please let me know if there are any troubles with this OneDrive shared link).https://attachment.outlook.office.net/owa/public_higher@outlook.com/service.svc/s/GetAttachmentThumbnail?id=AQMkADAwATNiZmYAZC1jNmNlLTE2OGMtMDACLTAwCgBGAAAD3jS4PtO4ok6emPsLe6htlgcAd9w%2BY5sSX0K4%2BOeRrODdowAAAgEMAAAAd9w%2BY5sSX0K4%2BOeRrODdowAAAIXlKJMAAAABEgAQAHmbmwDZF2QfSJuz3GK7atQD&thumbnailType=2&X-OWA-CANARY=X_OT8YKlV0CGEMSgsZMqO1DhIcR9NNQYGiGywSgDMPT37u9qjvf4GJ3S3p3X3gctYx7SfiNwtNY.&token=19efa433-21fa-4114-a44b-89c5a952a124&owa=outlook.live.com&isc=1
Question: Compute absolute value of current density at point S which lies at the exact center (30 meters from right and left sphere's center).

Homework Equations

In the previous question I had to compute total current flow through this system. I managed to find it resistance of the sea R_sea = (1/r_left + 1/r_right) / (2πγ) which I then plugged into I = U / (R_sea + R_load). It gave me I ≅ 72.2 A.

The Attempt at a Solution

I know that I = ∫JdS and J = γE, but from here on, I'm completely lost. Can somebody please help me, or at least give me a solid hint?

 

[BvU]

Hello pA,

No quick responses, so let me inform you that I don't see any picture or link.

Furthermore 72 A from a 300 V with an internal R of 4 Ohm seems a bit unlikely. You sure this r_left and r_right (what are they?) gave you the correct answer ?

 

[peroAlex]

Here's the link https://drive.google.com/file/d/0ByeYlJxPvdrUb3JkNm5UR2FjaUE/view?usp=sharing. I hope this will work! :)

Anyway, this task comes with solutions, but not path towards solution. I managed to obtain current 72.2 amperes from some PDF file which had similar example. Unfortunately, current density was never mentioned in there.

So yes, current comes from I = U / (R_load + R_sea) which returns I ≅ 72.2 A. I double checked my calculations and it returns correct value. Correct result should be J ≅ 0.0255 A/m^2.

 

[BvU]

Link works. The underwater field is equal to the field from a dipole (two spheres with opposite potential) . Any analogy you can think of to find the current density ?

It made me think of the electrolytic trough -- but I couldn't find a description with the formulas, just ads. (Unless your german is good enough)

 

[peroAlex]

Well, I must admit that my German is a bit rusty, but in the abundance of translator tools I think I will be able to pull through. Thank you so much for your time and willingness to share your knowledge! I finally understand the task.