# Electric field due to distributed planar charge

• easybakeoven

#### 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.

E=kQ/r^2

## 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

I guess you could do that though I am 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.