Gauss Law Problem to determine F/A

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SUMMARY

The discussion focuses on calculating the force per unit area (F/A) on three parallel charged sheets using Gauss's Law. The surface charge densities are 7.9 nC/m² for sheet I, -3.3 nC/m² for sheet II, and 5.4 nC/m² for sheet III. The correct approach involves using the electric field equations derived from Gauss's Law, specifically E = σ/2ε₀, to find the forces acting on each sheet. The calculated force per unit area for sheet I is 1.47 x 10^-6 N/m², while further calculations for sheets II and III require adjustments based on their respective charge densities.

PREREQUISITES
  • Understanding of Gauss's Law and its application in electrostatics.
  • Familiarity with electric field equations and surface charge density concepts.
  • Knowledge of the permittivity of free space (ε₀) and its significance in calculations.
  • Basic algebra and calculus skills for manipulating equations and integrating where necessary.
NEXT STEPS
  • Study the derivation of electric fields from surface charge densities using Gauss's Law.
  • Learn how to calculate forces between charged sheets in electrostatic scenarios.
  • Explore the concept of superposition in electric fields to analyze multiple charge distributions.
  • Investigate the role of permittivity in electric field calculations and its impact on force measurements.
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Students and professionals in physics, particularly those specializing in electrostatics, as well as educators seeking to clarify concepts related to electric fields and forces between charged objects.

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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. E=F/Q; Int(E) dA=Q/epsilon; [tex]\sigma=Q/A[/tex]
3. I combined the above eq and got this:
\sigma*(\sigma)/(2epsilon)
 
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The attempt I have done:

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

or
FI/A = -σσ’/εo= (3.26x10^-6),

FII/A = -σσ’/εo + σσ”/εo

FIII/A = σ’σ”/εo


---IT IS NOT RIGHT! HELP ME!
 

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