- #1

mshahi

- 1

- 0

## Homework Statement

We are given a disk with negligible thickness, a radius of 1m, and a surface charge density of σ(x,y) = 1 + cos(π√x

^{2}+y

^{2}). The disk is centered at the origin of the xy plane. We are also given the location of a point charge in Cartesian coordinates, for example [0.5,0.5,2]. We need to find the electric field components (x,y,z) at the location of the point charge.

## Homework Equations

d##\vec E## = σdS/4πε

_{0}⋅ ##\hat r##/r

^{2}

## The Attempt at a Solution

My first thought was to make dS a thin ring centre origin. this would give dS=2πr'dr' where r' is the radius from the origin to the ring. I then thought the I could write r

^{2}as r'

^{2}+z

^{2}, and r' would also be equal to √x

^{2}+y

^{2}. Plugging this and σ into the integral just to find the magnitude of ##\vec E## we get:

∫ (1+cos(πr'))r'/(r'

^{2}+z

^{2}) dr'

However I have realized that this is wrong because a) the answer it gives is far to small to be reasonable, b) I think this calculation assumes a spherical field which it clearly isn't, and c) the relationship to find r in terms of r' and z only holds if the point charge is over the disk, which it isn't necessarily. I think I am meant to split the integral into x, y, and z components but am unsure of whether this is the correct approach. Now i am completely stuck, none of the notes I can find explain this, I even took out a book from the 1950s on electrostatics to try and find the way to solve this and I just cannot for the life of me find it anywhere! Any help would be very much appreciated!