Electric Potential of point outside cylinder

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Homework Help Overview

The discussion revolves around determining the electric potential at a point outside a charged cylinder, focusing on the geometry and charge density involved. Participants are examining the separation vector and its components in cylindrical coordinates.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning the definition of the separation vector in cylindrical coordinates and discussing the geometry of the charge distribution. There are attempts to clarify the radial component and its relation to the overall distance calculation.

Discussion Status

The discussion is ongoing, with participants providing insights into the geometry and suggesting that a complete statement of the problem would facilitate better assistance. Some have proposed potential expressions for the distance calculation while others are still seeking clarity on the definitions involved.

Contextual Notes

There is mention of a lack of symmetry in the problem setup, which may affect the approach to finding the electric potential. Participants are also navigating the implications of using cylindrical coordinates versus Cartesian coordinates.

jkthejetplane
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Homework Statement
So i am supposed to set up an integral with s (radial) and z to show the electric potential at a point. Part b wants you to calculate the integral in s direction and write in terms of dV/dz
Relevant Equations
V = 1/4piEps Integral (rho/r)dTau
1615001281803.png

Edit: Below is my work but i believe i have chosen the wrong values of the separation vector in the s direction. Any ideas as to what it should be?
1615000379193.png
 

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A complete statement of the problem would help us help you. What is the geometry of the charge density of the problem? Is it a thin cylinder? I guess not cause you write in your notes that there is no symmetry present. Please post a complete statement of the problem if possible.
 
Delta2 said:
A complete statement of the problem would help us help you. What is the geometry of the charge density of the problem? Is it a thin cylinder? I guess not cause you write in your notes that there is no symmetry present. Please post a complete statement of the problem if possible.
I edited it to put the whole original problem. thanks
 
##(h-z)^2+(R-s)^2##? How are you defining s?
 
haruspex said:
##(h-z)^2+(R-s)^2##? How are you defining s?
What do you mean? s is radial component in cylindrical
 
jkthejetplane said:
What do you mean? s is radial component in cylindrical
So what is the distance from (s, Φ, z) to (0, 0, h)?
 
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haruspex said:
So what is the distance from (s, Φ, z) to (0, 0, h)?
I believe that's my main question above if i am understanding you correctly. I am not sure how to define the separation vector. Right not i have it as (h-z)zhat + (r-s)shat but i am unsure on the s direction component...
 
I think the correct distance is $$|\vec{r}-\vec{r'}|=\sqrt{(h-z)^2+s^2}$$. If you do a simple figure it is straightforward pythagorean theorem.
 
jkthejetplane said:
I believe that's my main question above if i am understanding you correctly. I am not sure how to define the separation vector. Right not i have it as (h-z)zhat + (r-s)shat but i am unsure on the s direction component...
By symmetry, Φ doesn't matter, so it reduces to Cartesian: (s, z) to (0, h).
 
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