Gauss' Law for Infinite Sheets of Charge

[kazukamikaze]

Homework Statement

Three parallel, infinite, insulating planes (sheets) of charge are arranged as shown (see attached image). Note carefully the charge desnitties and distances given. From left to right the charge densities are -3σ, +σ, +σ. How does the magnitude of the electric field at point a compare to the magnitude of the field at point b?

Homework Equations

E = σ/2ε^₀

The Attempt at a Solution

From what I recall from my lecture, the E field of an infinite sheet of charge does not depend on distance. Second, I believe that the field lines look something like what I've drawn in the second attached image. For that reason, I argued the magnitude of A was larger than B as the charge density of the sheet is larger.

 

[Dick]

Homework Statement

Three parallel, infinite, insulating planes (sheets) of charge are arranged as shown (see attached image). Note carefully the charge desnitties and distances given. From left to right the charge densities are -3σ, +σ, +σ. How does the magnitude of the electric field at point a compare to the magnitude of the field at point b?

Homework Equations

E = σ/2ε^₀

The Attempt at a Solution

From what I recall from my lecture, the E field of an infinite sheet of charge does not depend on distance. Second, I believe that the field lines look something like what I've drawn in the second attached image. For that reason, I argued the magnitude of A was larger than B as the charge density of the sheet is larger.

Homework Statement

Homework Equations

The Attempt at a Solution

The field at A is going to be the sum of the fields from all three plates, isn't it?

 

[kazukamikaze]

The field at A is going to be the sum of the fields from all three plates, isn't it?

Based off what one of my classmates told me, the field at the two points should be equal.

The only way I can rationalize these answer is by taking the sum of the three plates. I'm just confused as to why this is done.

 

[Dick]

Based off what one of my classmates told me, the field at the two points should be equal.

The only way I can rationalize these answer is by taking the sum of the three plates. I'm just confused as to why this is done.

Because the plates don't block the fields coming from the other plates, if that's what the confusion is. You could also directly use Gauss' theorem.