Gauss Law question that ask for F/A?

Question

Three large, thin charged sheets are parallel to each other, as shown in the figure. Sheet I has a total surface charge density of 7.9 nC/m², sheet II has a charge density of -3.3 nC/m², and sheet III has a charge density of 5.4 nC/m². 
Figure: ----------------(I)----------------(II)----------------(III) 
I would like to estimate the magnitude of the force per unit area on sheets I, II, and III (in N/m²). I am unsure how to begin this calculation. 
Attempt: E = F/Q; ∫(E) dA = Q/ε₀.

Luis McCullough · Accepted Answer

The electric field for a charged sheet is given by: E = σ/2εo

The force per unit area on sheet I due to sheet II is:

F = q’E = σ’AE => F/A = σ’E = σ’(σ/2εo) = 3.3x10^-9(7.9x10^-9)/2*8.85x10^-12

F/A = 1.47x10^-6 N/m²

The force per unit area on sheet II due to sheet I is: F/A = -1.47x10^-6 N/m²

The force per unit area on sheet II due to sheet III is:

F = σ’’E = 5.4x10^-9(-3.3x10^-9/2*8.85x10^-12 = -1x10^-6 N/m²

The total force per unit area on sheet II is: F/A = -2.47x10^-6 N/m²

The force per unit area on sheet III due to sheet II is:

F/A = σ’E = σ’(σ/2εo) = 3.3x10^-9(5.4x10^-9)/2*8.85x10^-12 = 1x10^-6 N/m²

Anonymous · Answer

I know this question is very old, but I figured it out. Jacy has the right idea, but when I used it, I got the question wrong.

So the equation we ll be using is E = σ’(σ/2εo)

I like to substitute these numbers as variables to make it a lot easier.

A = 7.9 x 10^-9 C/m^2

B = -3.3 x 10^-9 C/m^2

C = 5.4 x 10^-9 C/m^2

E = 8.85 x 10^-12

For the magnitude of the force per unit area on sheet I:

(AB) / (2E) = -1.47 x 10^-6 N/m^2 -> X

(AC) / (2E) = 2.41 x 10^-6 N/m^2 -> Y

Then we add both of them together, to get

X + Y = 9.37 x 10^-7 N/m^2

(direction is up)

For the magnitude of the force per unit area on sheet 2:

(BA) / (2E) = -1.47 x 10^-6 N/m^2 -> X

(BC) / (2E) = -1.00 x 10^-6 N/m^2 -> Y

Then we subtract both of them together, to get

X - Y = 4.66 x 10^-7 N/m^2

(the actual answer is negative, but we take the absolute value)

(direction is up as well)

For the magnitude of the force per unit area on sheet 3:

(CA) / (2E) = 2.41 x 10^-6 N/m^2 -> X

(CB) / (2E) = -1.00 x 10^-6 N/m^2 -> Y

Then we add both of them together, to get

X + Y = 1.40 x 10^-6 N/m^2

I hope this helps! I was looking everywhere for help but I ended up figuring it out 😀

Prof. Annamarie Hansen DDS

Gauss Law question that ask for F/A?

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