Electric Potential of point outside cylinder

In summary, the problem involves determining the separation vector for a charge density in a cylindrical geometry without symmetry. The distance between two points is found to be (h-z)^2 + s^2, with s being the radial component defined in cylindrical coordinates. The question of defining the separation vector remains, with the suggestion to simplify it by reducing to Cartesian coordinates.
  • #1
jkthejetplane
29
4
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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  • #2
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.
 
  • #3
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
 
  • #4
##(h-z)^2+(R-s)^2##? How are you defining s?
 
  • #5
haruspex said:
##(h-z)^2+(R-s)^2##? How are you defining s?
What do you mean? s is radial component in cylindrical
 
  • #6
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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  • #7
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...
 
  • #8
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.
 
  • #9
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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Related to Electric Potential of point outside cylinder

1. What is the formula for calculating the electric potential of a point outside a cylinder?

The formula for calculating the electric potential of a point outside a cylinder is V = kQ/r, where V is the electric potential, k is the Coulomb's constant, Q is the charge of the cylinder, and r is the distance from the point to the center of the cylinder.

2. How does the electric potential change as the distance from the cylinder increases?

The electric potential decreases as the distance from the cylinder increases. This is because the electric field strength decreases with distance, and the electric potential is directly proportional to the electric field strength.

3. Can the electric potential of a point outside a cylinder ever be negative?

Yes, the electric potential of a point outside a cylinder can be negative if the charge of the cylinder is negative. This means that the electric potential energy of a positive charge placed at that point would decrease, indicating a negative potential.

4. How does the radius of the cylinder affect the electric potential at a point outside the cylinder?

The radius of the cylinder has a direct effect on the electric potential at a point outside the cylinder. As the radius increases, the electric potential decreases, and vice versa. This is because a larger radius means a larger distance from the center of the cylinder, resulting in a weaker electric field.

5. Can the electric potential of a point outside a cylinder ever be zero?

Yes, the electric potential of a point outside a cylinder can be zero if the charge of the cylinder is zero or if the point is located on the axis of the cylinder. This means that the electric potential energy of a charge placed at that point would be zero, indicating no potential difference.

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