# Electric field due to distributed planar charge

1. Jan 29, 2009

### easybakeoven

An annulus (disk with a concentric hole) has inner and outer radii of R1 and R2 respectively, and uniform surface charge density of $$\sigma$$. the annulus lies in the xz plane with the y-axis centered in the hole.

a.) using the most basic expression of point charge electric field as a starting point, derive an expression for the electric field E at some distance Y above the annulus along the +Y-axis.

2. Relevant equations

E=kQ/r^2

3. The attempt at a solution

I started working on the problem, and I think that the equation I've come down to for the electric field in the y direction may be close to right....

E_y=K$$\lambda$$2$$\pi$$y*[-1/(r^2+y^2)^(1/2) + 1/(r^2+y^2)^(1/2)]

Is this close to right? I tried to work the problem by looking at a small linear slice of the annulus, and then rotating that around the y-axis

2. Jan 29, 2009

### chaoseverlasting

I guess you could do that though Im not sure of the math involved (I think you would use the cylindrical coordinate system to make it easier), Id find the electric field due to a ring of radius dr and then integrate that expression from r1 to r2.