Cylindrical Conductors Carrying a Current I -- Formula (?)

AI Thread Summary
The discussion focuses on finding a formula for cylindrical conductors carrying a current. It suggests modeling the conductor as if it has a full current throughout, while considering the effects of cavities that would carry an opposing current. Participants emphasize that in real-life scenarios, current flows on the outer surface of the conductor, and a uniform current distribution should be assumed for calculations. The conversation includes a mathematical expression using TeX markup to illustrate the relationship between the parameters involved. Overall, the thread aims to clarify the theoretical approach to modeling current in cylindrical conductors.
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Homework Statement
The current through the cylindrical conductor s I. Its cross sectional area is pi.a^2. Now, the two cavities on the figure above can be thought of as conductors carrying a current I' into the plane of the paper, where;
Relevant Equations
I'= [I/(pi.a^2)].pi.[a/2]^2
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How can I' be the formula above? Is there any formula to get this same
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The suggested path is to treat the situation as if you had a full current in the entire big conductor without the cavities, and then add in the effect of having an additional current going the other way where the cavities should be.

Did you try that?

IRL the current would be on the outer surface of the conductor ... it looks like you are supposed to model the current as uniform through the conductor (check).

Note: you can use TeX markup for equations ...

$$\frac{1}{\pi a^2}\pi \left(\frac{a}{2}\right)^2 = \frac{1}{4}$$

The code fopr that was
Code:
$$\frac{1}{\pi a^2}\pi \left(\frac{a}{2}\right)^2 = \frac{1}{4}$$
 
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