Gauss Law Problem to determine F/A

In summary, we have three parallel charged sheets with different surface charge densities, 7.9 nC/m^2 for sheet I, -3.3 nC/m^2 for sheet II, and 5.4 nC/m^2 for sheet III. We can estimate the magnitude of the force per unit area on each sheet by using the equation E=F/Q and integrating over the surface area of each sheet. Combining this equation with the equation for surface charge density, we get F/A = σ’E = σ’(σ/2εo). Using this, we can calculate the force per unit area on each sheet: 1.47x10^-6 N/m² for sheet I due to sheet II
  • #1
max190us
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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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  • #2


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!
 

What is Gauss Law and how is it used in determining F/A?

Gauss Law is a principle in physics that relates the electric flux through a closed surface to the charge enclosed by that surface. It is used to find the electric field at a point outside a charged surface by considering the distribution of charges within that surface.

What are the key steps in solving a Gauss Law problem to determine F/A?

The key steps in solving a Gauss Law problem are:
1. Identify the closed surface that encloses the charge
2. Determine the charge enclosed by the surface
3. Calculate the electric flux through the surface
4. Apply Gauss Law: Φ = Q/ε
5. Solve for the electric field at the desired point by rearranging the equation to E = Φ * ε / Q

How do I choose the appropriate Gaussian surface for a Gauss Law problem?

The Gaussian surface chosen should be symmetrical and should ideally have a constant electric field. Some common choices include spheres, cylinders, and cubes. It is important to choose a surface that encloses the charge and simplifies the calculation of the electric flux.

What are some common mistakes to avoid when solving a Gauss Law problem?

Some common mistakes to avoid when solving a Gauss Law problem are:
1. Not taking into account the direction of the electric field
2. Using the wrong units for charge or electric flux
3. Forgetting to account for the signs of the charges
4. Choosing an inappropriate Gaussian surface
5. Not considering the limits of the integral when calculating the electric flux

How can I check if my solution to a Gauss Law problem is correct?

You can check the correctness of your solution by following these steps:
1. Check if the units of your answer are correct
2. Verify if your solution satisfies the given conditions and assumptions
3. Recalculate the electric flux using a different Gaussian surface
4. Compare your solution with other known solutions or examples
5. If possible, use a simulation or experiment to validate your solution.

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