Potential inside a rectangular pipe

In summary, the independence of potential inside an infinite rectangular pipe along the z axis has to do with symmetry and the uniqueness theorem. The potential is not affected by changes in the z coordinate due to the uniformity of the structure. This topic was discussed in the PF schoolwork forums.
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TL;DR Summary: Independence of potential( inside a rectangular pipe running along z axis)from z coordinate

Consider the following diagram

Screenshot_2023-06-08-15-34-01-36_e2d5b3f32b79de1d45acd1fad96fbb0f.jpg

It is an infinite rectangular pipe running along z axis.I know that the potential inside the pipe is independent of z coordinate, but I cannot seem to convince myself of it.My guess is that it has to do something with uniqueness theorem.
 
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Welcome to PF. I've moved your thread to the schoolwork forums.

What equations would apply to this problem?
 
  • #3
better said:
My guess is that it has to do something with uniqueness theorem.
Symmetry, I'd have said. Everywhere along the axis looks like everywhere else.
 

1. What is potential inside a rectangular pipe?

The potential inside a rectangular pipe refers to the electric potential or voltage that exists within a pipe with a rectangular cross-section. This potential is created by the presence of charges inside the pipe and can be measured at any point within the pipe.

2. How is potential inside a rectangular pipe calculated?

The potential inside a rectangular pipe can be calculated using the formula V = kQ/r, where V is the potential, k is the Coulomb constant, Q is the charge inside the pipe, and r is the distance from the charge to the point where the potential is being measured.

3. What factors affect the potential inside a rectangular pipe?

The potential inside a rectangular pipe is affected by the amount and distribution of charges inside the pipe, as well as the size and shape of the pipe. The distance from the charges to the point where the potential is being measured also plays a role in determining the potential.

4. How does potential inside a rectangular pipe relate to electric fields?

The potential inside a rectangular pipe is directly related to the electric field inside the pipe. The electric field is the gradient of the potential, meaning that the electric field points in the direction of decreasing potential. This relationship is described by the equation E = -∇V, where E is the electric field and ∇V is the gradient of the potential.

5. Can the potential inside a rectangular pipe be negative?

Yes, the potential inside a rectangular pipe can be negative. This indicates that the electric field is pointing in the opposite direction of the potential gradient. In other words, the potential is decreasing in the direction of the electric field. This can occur when there are more negative charges inside the pipe than positive charges.

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