Electric Field GRE Problem

[PsychonautQQ]

Homework Statement

http://grephysics.net/ans/9277/64

I'm confused. How can there be a charge density if the electric field is one dimensional?

 

[Sunil Simha]

Think about charged sheets. What would be the electric field because of a charged sheet that is infinite in size?

 

[PsychonautQQ]

so there is an electric field through e_x and e_y but it comes from the e_z field? like it says e_x and e_y are zero but say there was a point (1,0,0) (x,y,z). The "sheet" in the field would make there be an electric field in the x?

I don't know if i'm saying what i'm thinking clearly. I mean it looks the problem states that there is NO E field in the x and y domains, and yet if there is an E field in the Z domain, there can still be an E field in the X and Y because it is a distance r away from the Z. Dig?

 

[Sunil Simha]

What if the sheet of charge is in the x-y plane and is infinite?

 

[nasu]

I don't know if i'm saying what i'm thinking clearly. I mean it looks the problem states that there is NO E field in the x and y domains, and yet if there is an E field in the Z domain, there can still be an E field in the X and Y because it is a distance r away from the Z. Dig?

The "domain" is a region of space. There are no ex and ey domains.
Every point in the domain has coordinates x,y,z. The field is all along the z direction, in every point.
The field lines are all parallel to each other and to the z axis.
Te magnitude of the field changes linearly along the z axis.

Yous just need to see if this field can satisfy Maxwell's equations, and if it can, in what conditions.

 

[Sunil Simha]

Sorry about my previous reply. There was power shortage in my area. Ignore that reply completely. Try calculating the charge density in such a space. It weirdly turns out to be a constant. This means there is a uniform charge distribution throughout the space. I really don't think you can go in the reverse direction (assuming a uniform charge distribution in space and finding the field proportional to z). This seems very weird. The only positive thing here is that there does exist a charge density.