Finding electrostatic potential from charge distribution

[Plaetean]

Homework Statement

Question

Homework Equations

Equation

The Attempt at a Solution

Attempt I am not sure how to write the |r-r'| in a way that allows me to actually solve the integral. I have tried writing |r-r'| in spherical co ords, but all I seem to be able to get is this as the separation distance, which seems impossible to integrate. Any help on whether I have gone about the problem the wrong way, or a way to write |r-r'| in a more manageable form would be very much appreciated

 

[TSny]

Are you required to first find the potential using the formula you gave? Or, are you allowed to find E using some other equation (or law)?

 

[Plaetean]

No, perhaps I could do it just using Gauss' law instead, might be easier

 

[TSny]

No, perhaps I could do it just using Gauss' law instead, might be easier

Yes, give it a try.

 

[paranormal]

.

I understand your struggle with finding a manageable form for |r-r'| in the integral. Depending on the specific charge distribution and the desired location of the electrostatic potential, there are different approaches that can be taken to simplify the integral. One method is to use a coordinate system that is appropriate for the given charge distribution, such as cylindrical or spherical coordinates. Another approach is to use symmetry arguments to reduce the integral to a simpler form. Additionally, numerical methods can also be used to approximate the integral if an analytical solution is not possible. It may also be helpful to consult with a colleague or refer to resources such as textbooks or online tutorials for guidance on solving similar integrals.