Electric field between two plates

[Robin Lee]

1. Positive and negative charges are distributed evenly in two parallel plates with width "w". The density of the positive and negative charge is +$$\rho$$ and -$$\rho$$. Assume that the length of the plates at y direction is $$\infty$$

(a) Find the electric field in the plates
(b) Let the electric potential at x=-w equal to 0, find the electric potential in the plates.

Homework Equations

$$\Delta$$E=k*Delta-Q*r/r² where r is the unit vector -- (1)


3. My approach
I sliced an infinitesimal portion of the plate horizontally denoted as Delta-y and represent the charge Delta-Q = rho *Delta-y*2*w. Is my expression for Delta-Q correct?

r is the observation point which is at opposite to the portion Delta-y on the negative plate of which magnitude is "w".

Substitute my expression for Delta-Q into (1), I obtain Delta-E = k*rho/w.

Do I have to integrate Delta-E from -infinity to +infinity to obtain the electric field in the plates? If so, I will get E=0. Does this make sense?

Thank you.

 

[kuruman]

This is a Gauss's Law problem. Use the standard "pillbox" with its faces perpendicular to the x-axis.

 

[Robin Lee]

This is a Gauss's Law problem. Use the standard "pillbox" with its faces perpendicular to the x-axis.

I obtained $$\rho$$*2w/vacuum permittivity. I also did a sanity check that the unit is correct.

Thanks for the guidance. Now I learned that for highly symmetric problem, Gauss's Law really makes the problem much easier than using Biot-Savart Law.