- #1

Karl Karlsson

- 104

- 12

- Homework Statement
- A rod with a circular center in the middle (which causes the rod to change direction by 90 °) has an evenly distributed linear charge density 𝜆 of electrons along the entire rod. Determine the electrical potential of the red dot in the figure below which is at the center of the circular round. The reference potential is 0 V far away from the rod.

- Relevant Equations
- See below

A rod with a circular center in the middle (which causes the rod to change direction by 90 °) has an evenly distributed linear charge density 𝜆 of electrons along the entire rod. Determine the electrical potential of the red dot in the figure below which is at the center of the circular round. The reference potential is 0 V far away from the rod.

Given values are radius R, length a and charge density 𝜆.

My attempt:

Sorry for writing my solution not in english but you get the idea. As one can see the integral gets very complicated when i am trying to come up with an expression for the force at point (d,0). And then i haven't even started doing the integral for the potential difference of the given point and point (d,0). There must be an easier way to solve this problem.

Thanks in beforehand!

Given values are radius R, length a and charge density 𝜆.

My attempt:

Sorry for writing my solution not in english but you get the idea. As one can see the integral gets very complicated when i am trying to come up with an expression for the force at point (d,0). And then i haven't even started doing the integral for the potential difference of the given point and point (d,0). There must be an easier way to solve this problem.

Thanks in beforehand!