Trying to compute electro static field

[oronanschel]

Homework Statement

i tried to compute the electrostatic field of a charged ring at a point not
in the center

i have problem with transforming from xy to polar system
what do you think about this try?

Homework Equations

The Attempt at a Solution

 

[Nate810]

The electrostatic field of a charged ring can be computed by using Gauss's law. This states that the total electric flux passing through any closed surface is equal to the total charge enclosed within the surface divided by the permittivity of free space. To calculate the electrostatic field at a point not in the center, we need to transform from the Cartesian coordinates (x and y) to polar coordinates (r and θ). This is done by using the following equations: x = r cos θ y = r sin θ We then use these equations to calculate the electric field at the point in question.