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

In summary, the suggested path is to treat the situation as if there was a full current in the entire conductor without the cavities, and then add the effect of an additional current going the opposite direction where the cavities would be. It is recommended to model the current as uniform through the conductor and the equation for that is given by $\frac{1}{\pi a^2}\pi \left(\frac{a}{2}\right)^2 = \frac{1}{4}$.
  • #1
requied
98
3
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
1592927337236.png

1592927385542.png


How can I' be the formula above? Is there any formula to get this same
1592927476652.png
 
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  • #2
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:
$$\frac{1}{\pi a^2}\pi \left(\frac{a}{2}\right)^2 = \frac{1}{4}$$
 

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

1. What is the formula for calculating the magnetic field inside a cylindrical conductor carrying a current?

The formula for calculating the magnetic field inside a cylindrical conductor carrying a current is B = μ0I/2πr, where B is the magnetic field, μ0 is the permeability of free space, I is the current, and r is the distance from the center of the conductor.

2. How do you determine the direction of the magnetic field inside a cylindrical conductor carrying a current?

The direction of the magnetic field inside a cylindrical conductor carrying a current can be determined using the right-hand rule. If you point your thumb in the direction of the current, your fingers will curl in the direction of the magnetic field.

3. What is the significance of the radius in the formula for the magnetic field inside a cylindrical conductor carrying a current?

The radius in the formula for the magnetic field inside a cylindrical conductor carrying a current represents the distance from the center of the conductor. This distance affects the strength of the magnetic field, with the field being stronger closer to the center and weaker further away.

4. Can the formula for the magnetic field inside a cylindrical conductor carrying a current be used for any shape of conductor?

No, the formula for the magnetic field inside a cylindrical conductor carrying a current is specifically for a cylindrical shape. Different shapes of conductors will have different formulas for calculating the magnetic field.

5. How does the current affect the strength of the magnetic field inside a cylindrical conductor?

The current is directly proportional to the strength of the magnetic field inside a cylindrical conductor. This means that as the current increases, the magnetic field also increases, and vice versa.

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