Electric potential distribution of a charged circular rod

[kth]

Homework Statement

Im trying to calculate the electric potential created by a circular rod of charge Q and radius R at a random point (not only on the rod's axis). The rod can be considered very thin.

Homework Equations

The Attempt at a Solution

V = k \int dq/r
My problem is how to express r in a better way. I know i have to use cylindrical coordnates (r,z) but how can i express the distance from the charge element dq when the point P is not on the rods axis?

 

[anathema]

Hello there,

To calculate the electric potential at a point that is not on the rod's axis, you can use the distance formula in cylindrical coordinates:

r = √(x^2 + y^2)

Where x and y are the coordinates of the point P. This will give you the distance from the charge element dq to the point P.

Another approach would be to use the Pythagorean theorem to find the distance between the charge element and the point P:

r = √(z^2 + (R - x)^2)

Where z is the distance from the center of the rod to the point P and x is the distance from the center of the rod to the charge element dq.

I hope this helps! Let me know if you have any other questions.

 

[nlightner]

I would suggest using the formula for electric potential in cylindrical coordinates, which is V = kλln(r/R), where λ is the linear charge density of the rod and R is the radius of the rod. This formula takes into account the distance from the charge element dq to the point P, which is represented by the natural logarithm term. Additionally, since the rod is considered very thin, we can assume that the linear charge density is constant throughout the rod. Therefore, the formula can be simplified to V = kQln(r/R)/L, where Q is the total charge of the rod and L is the length of the rod. This formula should give you the electric potential at any point P, even if it is not on the rod's axis.