Hello,
I would like to know how to deduce the amount of current flowing through a solid volume , when current is applied in the form of current density 'J' (A/m2).
Example: As shown in the image attached, the solid body is a rectangular volume which acts as a coil in a electromagnet. In the simulation model I am building , the current flowing through the coil has to be input in terms of current density. The total volume is about 4.5 x e-6 m3 . A current density of 1e6 A/m2 is applied to the body.
As current density J=I/A , if applied to a 2D surface area, it is pretty straight forward to calculate the current flowing through the area.
What is the formulation to calculate the current in amperes for the volume?
Hi Vivek Kishen Haridas ,
in the equation J = I / A, I is aligned normal to the area A. If the direction of the current is known, one has to choose a surface that is perpendicular to the direction of the current.
If your picture represents a usual coil, then the four parts form a closed circuit. The cross-sections of each of the four parts seem to be of equal magnitude, so you have to choose one of them as area A.
In exercises like this, you don't have to worry about the corners. Here, the actual cross-section is larger but you can treat the corners as if the current would change its direction in one 90° step.
Hi Vivek Kishen Haridas ,
in the equation J = I / A, I is aligned normal to the area A. If the direction of the current is known, one has to choose a surface that is perpendicular to the direction of the current.
If your picture represents a usual coil, then the four parts form a closed circuit. The cross-sections of each of the four parts seem to be of equal magnitude, so you have to choose one of them as area A.
In exercises like this, you don't have to worry about the corners. Here, the actual cross-section is larger but you can treat the corners as if the current would change its direction in one 90° step.
When calculating the current density, the volume is not relevant. What you need is the cross-section of your setup. Assuming that the long and the short segments are of the same height and width, multiply height and width to get the cross-section's size.
As you already wrote: it's quite straight forward.
Joerg Fricke U. Dreher , thank you for your valuable inputs. I guess it is clear now. So according to my undersanding, the current flowing through the volume is the current flowing normal to the cross-sectional area at any given section in the volume and it remains the same for any cross section along the same direction?
Vivek Kishen Haridas , yes, the DC current in a closed circuit without any branches is everywhere the same, due to charge conservation.
Of course, if the area of the cross-section is different at different locations, then the current density differs, too.
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