Finding the E-field between two infinite plane charged sheets

[aximwolf]

Homework Statement

Two infinite-plane non-conducting, thin sheets of uniform surface charge p1 = 13.35 uC/m2 and p2 = -8.65 uC/m2) are parallel to each other and d = 0.245 m apart. (As shown in the diagram below.) What is the electric field between the sheets? (Note: the field is positive if it is parallel to the vector x).

Homework Equations

Sigma/2*epsilon_not

Epsilon not = 8.85e-12 (SI Units)

The Attempt at a Solution

The distance between the sheets should not matter in calculating the E-field between them because the E-field between them is uniform. We are given two sigmas and since the net charge on the field is toward the negative plane we just sum the two over 2*epsilon_not, and Epsilon not is a constant.

sigma1=13.35e-6 C/m^2
sigma2=-8.65e-6 C/m^2

(sigma1 + sigma2)/(2*epsilon_not) = E-field
(13.35e-6 + 8.65e-6)/(2*epsilon_not) = 1.2e6 N/C
Than since the E-field is perpendicular to the planes, but pointing in the opposite direction of positive X the answer becomes negative.
Answer: -1.2e6 N/C (unfortunately I tried this and did not get the problem right)

What did I get wrong?

 

[SammyS]

In the region between the sheets:

What is the direction of the E field due to the σ₁ sheet?

What is the direction of the E field due to the σ₂ sheet?​

 

[aximwolf]

The E-field on sigma1 is going -x and so is sigma2 right?

 

[gneill]

Is the marking software fussy about significant figures?

 

[SammyS]

The E-field [STRIKE]on[/STRIKE] due to sigma1 is going -x and so is sigma2 right?

Right, so you should have a negative plus a negative.

 

[aximwolf]

Right but that doesn't change the answer numerically am I forgetting a step?

 

[Doc Al]

Right but that doesn't change the answer numerically am I forgetting a step?

Why did you express your answer to only 2 sig figs? (To repeat what gneill already pointed out.)

 

[aximwolf]

More sig figs worked thank you everyone!

 

[SammyS]

Right but that doesn't change the answer numerically am I forgetting a step?

You have:

E-field due to sigma₁=13.35e-6 C/m²
E-field due to sigma₂=-8.65e-6 C/m²​

But, if they're both pointing left (as vectors), then they should both be negative !

E₁ + E₂ = -13.35×10^-6 + -8.65×10^-6 = ____ ?

 

[aximwolf]

yes that's the way I ended up doing it -13.35e-6+-8.65e-6

 

[SammyS]

That's stange, I don't see that result anywhere in this thread.