Potential at all points due to uniformly charged infinite cylinder

In summary, an infinitely long cylinder with uniform charge ρ and radius R has its electric potential calculated at all points in space. The integral formula for potential with a reference point at r=∞ would diverge in this case, so an arbitrary r' vector is chosen as the reference point to solve the problem as usual. However, it is recommended to show the work in order to have a better understanding of the solution.
  • #1
oddjobmj
306
0

Homework Statement


Infinitely long cylinder of radius R with uniform charge ρ. Calculate the electric potential at all points in space.


Homework Equations



V(a)-V(b)=-∫ba[itex]\vec{E}[/itex]([itex]\vec{r}[/itex]')°dr'[itex]\hat{r}[/itex]

The Attempt at a Solution



Generally potential is calculated with a reference point at r=∞ but in the case of an infinite cylinder I believe the integral above would diverge because the potential at ∞ (V(∞)) would not necessarily equal zero. What I did then is simply provide an arbitrary r' vector as the reference point and went through the problem as one would normally do so with a non-infinite charged object. Is this okay? Do I have to do something extra because of the non-zero reference point?

Thank you!
 
Physics news on Phys.org
  • #2
It is right, but better to show your work.

ehild
 

1. What is the formula for calculating the potential at any point due to a uniformly charged infinite cylinder?

The formula for calculating the potential at any point due to a uniformly charged infinite cylinder is V = (λ/2πε0) ln(r/r0), where V is the potential, λ is the charge density, ε0 is the permittivity of free space, r is the distance from the point to the cylinder, and r0 is the radius of the cylinder.

2. How does the potential at a point change as the distance from the cylinder increases?

As the distance from the cylinder increases, the potential at a point decreases. This is because the electric field strength decreases with distance, and potential is directly proportional to electric field strength.

3. Can the potential at a point due to a uniformly charged infinite cylinder ever be zero?

Yes, the potential at a point can be zero if the point is located at a distance of r0 from the cylinder. This is because ln(r/r0) would equal zero, resulting in a potential of zero.

4. How does the charge density of the cylinder affect the potential at a point?

The charge density of the cylinder directly affects the potential at a point. As the charge density increases, the potential at a point also increases. This is because the electric field strength and potential are directly proportional to charge density.

5. Is the potential at a point due to a uniformly charged infinite cylinder affected by the radius of the cylinder?

Yes, the potential at a point is affected by the radius of the cylinder. As the radius increases, the potential at a point decreases. This is because the electric field strength decreases with distance from the cylinder, and the potential is directly proportional to electric field strength.

Similar threads

  • Introductory Physics Homework Help
2
Replies
64
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
780
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
4K
  • Introductory Physics Homework Help
Replies
1
Views
933
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
23
Views
257
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
2K
Back
Top