Current density of specific configuration

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Homework Help Overview

The problem involves two hollow metal spheres submerged in seawater, with specific parameters including their radii, distance apart, and a voltage source. The objective is to compute the current density at a specific point between the spheres.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculation of total current flow and the relationship between current density and electric field. There are questions about the validity of the current value obtained and the definitions of certain variables.

Discussion Status

Some participants have provided guidance on the relationship between current density and electric field, while others are exploring analogies to better understand the problem. There is acknowledgment of differing interpretations and calculations without a clear consensus on the approach to take.

Contextual Notes

Participants note that the task comes with solutions but lacks a clear path to reach those solutions. There is mention of a potential analogy involving dipoles and electrolytic setups, but specifics are still under discussion.

peroAlex
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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?
 
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Hello pA, :welcome:

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 ?
 
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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.
 
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)
 
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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.