# Current density of specific configuration

• peroAlex
In summary, the two half-submerged metal spheres have a specific conductance of γ = 4 S/m. They are connected to a real voltage source (U = 300V and R = 4Ω). The distance between their centers is much greater than their radii dimensions and equals 60 meters. The spheres are half-submerged in the sea water with a current density of J = 0.255 A/m^2.
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).
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?

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

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)

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.

## 1. What is current density of specific configuration?

Current density of specific configuration refers to the measure of electric current per unit area in a specific configuration or arrangement of conductors. It is often denoted by the symbol J and is expressed in units of amperes per square meter (A/m²).

## 2. How is current density of specific configuration calculated?

Current density of specific configuration is calculated by dividing the total current flowing through a specific area by the area itself. Mathematically, it can be represented as J = I/A, where J is the current density, I is the total current, and A is the area.

## 3. What are the factors that affect current density of specific configuration?

The main factors that affect current density of specific configuration are the type of material, its conductivity, and the cross-sectional area. Materials with higher conductivity will have a higher current density, while a larger cross-sectional area will result in a lower current density.

## 4. Why is current density of specific configuration important?

Current density of specific configuration is important because it helps in understanding the distribution of current in a particular system. It is also used to determine the heating effect of electric current, as higher current densities can lead to overheating and potential hazards.

## 5. How can current density of specific configuration be controlled?

Current density of specific configuration can be controlled by adjusting the area or the amount of current flowing through the system. Using materials with higher conductivity can also help in controlling the current density. Additionally, using appropriate insulation and heat dissipation techniques can also help in controlling the current density.