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The problem involves two large, nonconducting plastic sheets carrying uniform charge densities, and you're asked to use Gauss's law to find the magnitude and direction of the electric field at a point 125 cm from the inner surface of the right-hand sheet.

Let's break down the given information:

1. **Charge Densities (Surface Charge Densities):**
   - \(\sigma_1 = -5.40 \, \mu C/m^2\) (Left inner surface)
   - \(\sigma_2 = 5.00 \, \mu C/m^2\) (Left outer surface)
   - \(\sigma_3 = 3.00 \, \mu C/m^2\) (Right inner surface)
   - \(\sigma_4 = 4.00 \, \mu C/m^2\) (Right outer surface)

2. **Thickness of each plastic sheet:** \(10.0 \, \text{cm}\)

3. **Point B is located 125 cm from the inner surface of the right-hand sheet.**

We will calculate the electric field at point B using the **principle of superposition** and **Gauss's law**.

### Steps:
1. **Gauss's Law** states that the electric field due to an infinite sheet of charge is given by:
   \[
   E = \frac{\sigma}{2\epsilon_0}
   \]
   where \(\sigma\) is the surface charge density and \(\epsilon_0\) is the permittivity of free space (\(8.85 \times 10^{-12} \, C^2/(N \cdot m^2)\)).

2. **Consider the electric fields generated by each surface:**
   - The electric field due to \(\sigma_1\) and \(\sigma_2\) (left sheet) will contribute to the overall field at point B.
   - Similarly, the electric field due to \(\sigma_3\) and \(\sigma_4\) (right sheet) will also contribute.

3. Since point B is on the right-hand side (far from the sheets), we consider the combined contributions from all the charge densities to determine the net field.

Let's proceed with the calculation.

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Do you want to go into the detailed step-by-step solution?

Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities σ1, σ2, σ3, and σ4 on their surfaces. The charge densities are σ1 = -5.40 μC/m^2, σ2 = 5.00 μC/m^2, σ3 = 3.00 μC/m^2, and σ4 = 4.00 μC/m^2. Use Gauss's law to find the magnitude and direction of the electric field at point B, which is 125 cm from the inner surface of the right-hand sheet.

This problem uses Gauss's Law to calculate the electric field at a point near charged plastic sheets with known surface charge densities. Key concepts include the superposition principle and the formula E = σ / (2ε₀).

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