How can we solve the infinite sheet problem for electric field at a point P?

[latentcorpse]

http://www.ph.ed.ac.uk/teaching/course-notes/documents/76/1000-Jun2001.PDF

in q5, the second part of the question. How do we even start to do this? (it's the bit about finding the field if you assume that it's part of an infinitely large flat sheet of material)

my field from the first part of the question is

$E(P)=\frac{1}{4 \pi \epsilon_0} \frac{qd}{a}$

since $dE_z=\frac{dq}{4 \pi \epsilon_0}{\vec{a} \cdot \vec{\hat{z}}}{a^3}=\frac{1}{4 \pi \epsilon_0} \frac{dq a \cos{\theta}}{a^3}$ then i canceled the a's and subbed $\cos{\theta}=\frac{d}{a}$

 

[Astronuc]

I believe that problem concerning the infinite sheet means using a ring method of integration.

Each ring has charge C*2πr dr, and each ring contributes to the E-field at P.

For an infinite sheet, 0 < r < ∞

 

[latentcorpse]

im a bit confused - does that mean i get the total charge by $\int_0^{\infty} C 2 \pi r dr$?

 

[Astronuc]

Yes, but one wishes to find E(P), so one must dE from all the infinitesimal rings for 0 to ∞. Note that as r -> ∞, the angle from the vertical axis to the line from P to the ring of charge.