Gauss Law question that ask for F/A?

Three large but 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/m^2, sheet II a charge of -3.3 nC/m^2, and sheet III a charge of 5.4 nC/m^2.

Figure:

----------------(I)

----------------(II)

----------------(III)

Estimate the magnitude of the force per unit area on sheet I, II, and III, N/m^2.

**I do not know how to start**

Attempt: E=F/Q; Int(E) dA=Q/epsilon

2 Answers

  • 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

  • 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 😀

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