Magnitude and direction of electric field with nonconducting sheets

[cwbullivant]

Homework Statement

Two very large, non-conducting sheets, each 10cm thick, carry uniform charge densities δ₁ = -6.00μC/m^2, δ₂ = +5.00μC/m^2, δ₃ = +2.00μC/m^2, δ₄ = 4.00μC/m^2. Use Gauss's law to find the magnitude and direction of the electric field at points A, B, and C, far from the edges of these sheets.

a) Point A, 5.00cm from the left face of the left-hand sheet

b) Point B, 1.25cm from the inner surface of the right-hand sheet

c) Point C, in the middle of the right hand sheet

Homework Equations

Presumably

$$ E = \frac{\sigma}{2\epsilon} $$

The Attempt at a Solution

I took the indication from the problem statement "far from the edges of those sheets" to imply that the answer would be achieved using the formula for electric field due to an infinite plane of charge, for points close to the sheet (i.e. the distance from the sheet is small relative to the length of the sheet), which was derived from Gauss' law in an earlier lecture.

The only thing I'm wondering with this is that the formula, given above, seems to imply that the electric field at those points is completely independent of the distance of the point from the charges edges; this seems reasonable, given the assumption that the ratio of the distance of the point from the edge is very small compared to the length of the sheet itself (only the width of 10cm is given).

The problem I have accepting this idea is the fact that the width of the sheets, as well as the distance of the points from the sheets is given; combined with the $$ \frac{1}{r^2} $$ nature of the electric field equation, it seems problematic to have a solution which is independent of distance.

 

[mfb]

As the size of the sheets is not given and it is described as "very large", I think you can approximate them as infinite sheets. The size of the sheets could be given to make clear where (in which region) the points are, but I guess the sketch does the same job.

The solution is independent of the distance values.