Charge density, electric fields

[glid02]

Here's the question:
A square plate of copper with 50.6 cm sides has no net charge and is placed in a region of uniform electric field of 80.9 kN/C directed perpendicularly to the plate.

a. Calculate the charge density of each face of the plate.

b. Calculate the total charge on each face.

I know I can find the total charge with density*area, and I know that density = Q/A, I just don't know how to convert the field into a charge, and I'm not even sure if that's what I'm supposed to do. Any help would be great.

Thanks a lot

 

[OlderDan]

Have you encountered the idea of a Gaussian pillbox?

 

[glid02]

That exact term hasn't been used but I have learned about Gaussian surfaces. The only example in my book that even somewhat deals with this question finds the electric field of a charged plane with a known density with a Gaussian cylinder.

 

[OlderDan]

That exact term hasn't been used but I have learned about Gaussian surfaces. The only example in my book that even somewhat deals with this question finds the electric field of a charged plane with a known density with a Gaussian cylinder.

This is a very similar problem to the plane of charge. If you use a Gaussian cylinder with cylinder walls perpendicular to a surface of the plate, one end inside the metal, and the other end outside the metal in the constant electric field the surface integral of the field is very easy to compute. The field inside the metal is zero. The field outside is parallel to the walls of the cylinder so they do not contribute. The only contribution is from the one circular end where the field is perpendicular to the surface and constant.

If you apply Gauss's law for cylinders cutting each side of the plate separately you can find the charge contained within the Gaussian cylinder for each surface. From this you can find the charge density of each plate. Using the charge density and the dimensions of the plate you can find the total charge on each face.