Why Can't the Potential Integral Formula Be Used for Infinite Line Charges?

[brad sue]

Hi ,
i have a question I don't know how to answer:

Explain why the potential integral formula cannot be used to directly determine the potential from an infinite uniform line charge ρlo that is on the z axis.

When we talk about it in class, I learn that the potential integral was used for finite displacement. I d read the textbook but I did not have other information.

So I there other reason to answer this question?

B.

 

[ranger]

Here is an interesting discussion about your question:
https://www.physicsforums.com/showthread.php?t=13665

 

[m2003]

Hi there,

Thank you for your question. The potential integral formula, also known as the Coulomb's law, is used to determine the electric potential at a point in space due to a finite point charge or a finite line charge. This formula is derived from the principle of superposition, which states that the total potential at a point in space is the sum of the potentials due to each individual charge.

In the case of an infinite uniform line charge on the z-axis, the charge extends to infinity in both directions and is not finite. This means that the potential at any point along the z-axis would also be infinite, making it impossible to calculate using the potential integral formula. Additionally, the potential integral formula assumes that the charge distribution is finite and continuous, which is not the case for an infinite line charge.

Furthermore, the potential integral formula is derived from the concept of a point charge, which has a defined position and magnitude. However, an infinite line charge does not have a specific point location and its charge is distributed along the entire line. This makes it mathematically impossible to use the potential integral formula to directly determine the potential at any point on the z-axis.

In summary, the potential integral formula cannot be used to directly determine the potential from an infinite uniform line charge on the z-axis because the charge distribution is infinite, not finite, and the formula is derived from the concept of a point charge which does not apply to an infinite line charge. I hope this helps answer your question. If you have any other questions, please let me know.