- #1

fluidistic

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## Homework Statement

Consider a slight annulus of radius b which lies in the x-y plane (its center is at the origin). Find the point on the positive z-axis in which the magnitude of the electric field is the greatest. The total charge of the annulus is Q.

## Homework Equations

None given.## The Attempt at a Solution

I've sketched the situation and I realize that if z=0 the electric field is null. Furthermore the electric field only has its component on the z-axis. So its magnitude is its projection onto the z-axis.

I tried to find the electric field for all points on the z-axis but without success.

I consider a differential part of the annulus of length dl, so its charge is [tex]\lambda dl[/tex]. I have that [tex]2\pi b \lambda=Q[/tex].

[tex]d\vec E = \frac{dQ}{r^2}\sin \theta[/tex] according to my draft (or is it cos?).

[tex]\vec E = 2\pi b \lambda \int \frac{\sin \theta}{r^2} dr[/tex]. But I'm stuck here, and I think I already made an error. [tex]\theta[/tex] represent the angle 0dlP where P is any point on the z-axis.

I don't know why I integrated this part, does [tex]E=\frac{2\pi b \lambda}{b^2}=\frac{2\pi \lambda}{b}[/tex] instead? (I could eventually replace lambda by what it's worth with respect to Q.) I'm sure not, E must depends on [tex]\theta[/tex], and if [tex]\thetha=0[/tex], E=0.

Can someone help me? Thanks!