Electrostatics - infinite plates

[Gil-H]

Homework Statement

Consider two infinite conducting plates of some thickness with charge 2q and -q.
The system is in equilibrium, which means there's no charged particles in motion.
Find the charge distribution on the surfaces of each plate.
(designated as q₁ q₂ q₃ and q₄)

Homework Equations

The Attempt at a Solution

All I know about infinite plates is that the electric field is σ/2ε₀.
But that doesn't seem to help me here

 

[Doc Al]

All I know about infinite plates is that the electric field is σ/2ε₀.
But that doesn't seem to help me here

Use that to figure out the field between the plates.

Hint: What's the field within the conducting material? Apply Gauss's law.

 

[Gil-H]

Thanks. You gave something to think about.
But I'm not sure I follow completely.

Because the field inside each plate is zero,
I used gaussian surface which encloses q₂ and q₃,
and that leads me to that:
q₂ + q₃ = 0,
and together with:
q₁ + q₂ = 2q
q₃ + q₄ = -q
I have three equations.

I need to get one more. How?

 

[Doc Al]

How about using some gaussian surfaces that enclose only one of the charges at a time?

 

[Gil-H]

Now I got that!
Thank you very much!

By doing that I achieved that:
q₁ + q₂ + q₃ = -q₄
q₂ + q₃ + q₄ = -q₁

and with:
q1 + q2 = 2q
q3 + q4 = -q

I ended up with:
q₁ = 0.5q
q₂ = 1.5q
q₃ = -1.5q
q₄ = 0.5q

which is the correct answer! :-)