Find the magnitude of the electric field at regions 2 and 3.

[Mason Smith]

Homework Statement

The three parallel planes of charge shown in the figure have surface charge densities (-1/2)η, η, and (-1/2)η.

Homework Equations

I think that the electric field is equal to eta divided by epsilon naught.

The Attempt at a Solution

Well, I know that the electric field at regions 1 and 4 are zero.
E₁ = E₄ = (-1/2)η + η + (-1/2)η = 0.
I know that the electric field in region 2 points upward and that the electric field at region 3 points downward. However, I am not sure how to calculate the electric field in these regions. How do I go about calculating the electric field in these regions?

 

[TSny]

Homework Equations

I think that the electric field is equal to eta divided by epsilon naught.

Check your notes. The field due to a single infinite plane of charge density $\eta$ is not $\frac{\eta}{\epsilon_0}$.

The Attempt at a Solution

Well, I know that the electric field at regions 1 and 4 are zero.

How do you know that? The reason I ask this question is that the logic for deducing that the field is zero in regions 1 and 4 is similar to the logic for finding the fields in regions 2 and 3.

 

[Mason Smith]

Check your notes. The field due to a single infinite plane of charge density $\eta$ is not $\frac{\eta}{\epsilon_0}$.How do you know that? The reason I ask this question is that the logic for deducing that the field is zero in regions 1 and 4 is similar to the logic for finding the fields in regions 2 and 3.

Oh, yes. I confused the electric field for an infinite plane of charge with the electric field of a conductor in electrostatic equilibrium.
Well, when I worked the problem by saying that E₄ = E₁, I got an answer of zero. I put that answer into MasteringPhysics. The answer was correct. Using that same reasoning with the electric field in regions 2 and 3 proved wrong.

 

[TSny]

Well, when I worked the problem by saying that E₄ = E₁, I got an answer of zero.

How did you get the answer of zero? What steps of reasoning did you use?