Plate conductor in electrostatic equilibrium

[member 392791]

Homework Statement

A thin, square, conducting plate 50.0 cm on a side lies
in the xy plane. A total charge of 4.00 x 10-8 C is placed
on the plate. Find (a) the charge density on each face of
the plate, (b) the electric field just above the plate, and
(c) the electric field just below the plate. You may assume
the charge density is uniform.

Homework Equations

σ = Q/A

The Attempt at a Solution

a) σ = 4×10^-8 / (.5)^2 / 2 = 8x10^-8 C/m^2
b) Ok using gauss law

E = σ / ε = 9.04 kN/C

c) my problem is why for part C, the answer is -9.04 kN/C. If my Gaussian surface is below the plane, its area vector is pointing downward, and my positive bottom surface charges electric field is also pointing down, so they are pointing in the same direction, thus E should be positive??

 

[TSny]

c) my problem is why for part C, the answer is -9.04 kN/C. If my Gaussian surface is below the plane, its area vector is pointing downward, and my positive bottom surface charges electric field is also pointing down, so they are pointing in the same direction, thus E should be positive??

What you should conclude is that the flux is positive for your Gaussian surface. The field is downward (as you stated) and I think that is all that is meant by the answer being negative.