Uniformly Charged Cylinder - Potential at distance d?

  • Thread starter acedeno
  • Start date
  • #1
36
2

Homework Statement


Consider a uniformly charged solid cylinder of radius R, length L and charge density ρ. Find the
potential at a distance d (> L/2) from the centre of the object, along the axis of the cylinder.

Homework Equations


V=∫kdq/r



The Attempt at a Solution


For me, it makes most sense to express this integral in cylindrical coordinates, seeing as the object is a cylinder. Also, since the axis of which the cylinder is on is not specified. I chose the z axis on a (x,y,z).

-stuff used for integration, respectively.
s[0,R]
Ø[0,2π]
z[0,L]

dq=sdsdØdz


I'm not too good at expressing notation on the computer so this is the basics of what i tried:

1st attempt: I know V(z)=∫E.dl , so, I tried to solve for E by using
E=∫kdq/r^2
E=∫∫∫(kρ/z^2)sdsdØdz

after I finished this integral, I lost confidence when doing the integral for V(z) because It didn't seem right to integrate over the same limits of integrations seeing as dl would be expressed as sdsdØdz - please tell me if i'm wrong.

2nd attempt: I just started with V=∫kdq/r.
V=∫∫∫(kρ/z)sdsdØdz
giving me
V(z)=kρπ*ln(z)*R^2

- I'm not sure which method is correct, if either. Help would be greatly appreciated.
- Also, since were just looking for the function with respect to a distance and because of the way the question was stated, I felt that it was okay to express r as just z rather than (L/2 + z)
 

Answers and Replies

Related Threads on Uniformly Charged Cylinder - Potential at distance d?

Replies
5
Views
7K
Replies
1
Views
1K
Replies
1
Views
2K
  • Last Post
Replies
4
Views
3K
Replies
1
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
2
Views
17K
Replies
5
Views
8K
Replies
4
Views
607
Replies
1
Views
1K
Top