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To solve this problem involving the electric fields between three charged sheets, we need to use the following principles:

### General Formula:
The electric field produced by an infinite sheet with surface charge density \( \sigma \) is given by:

\[
E = \frac{\sigma}{2\epsilon_0}
\]

Where:
- \( \sigma \) is the surface charge density of the sheet.
- \( \epsilon_0 \) is the permittivity of free space, \( \epsilon_0 = 8.854 \times 10^{-12} \, \text{C}^2/\text{N·m}^2 \).

Given:
- \( \sigma_A = +8.00 \, \text{nC/m}^2 \)
- \( \sigma_B = -4.00 \, \text{nC/m}^2 \)
- \( \sigma_C = +6.00 \, \text{nC/m}^2 \)

We are tasked with finding the **resultant electric field** at a point between sheets \( B \) and \( C \), located 2.00 cm from sheet \( B \).

### Step-by-Step Solution:

1. **Electric Field due to Sheet B:**
   Since the point of interest is to the right of sheet \( B \), and \( B \) has a negative surface charge, the electric field due to \( B \) will point towards \( B \) (i.e., in the negative \( x \)-direction).
   \[
   E_B = \frac{\sigma_B}{2\epsilon_0} = \frac{-4.00 \times 10^{-9}}{2 \times 8.854 \times 10^{-12}} = -225.88 \, \text{N/C}
   \]

2. **Electric Field due to Sheet C:**
   The point of interest is to the left of sheet \( C \), and \( C \) has a positive surface charge. Therefore, the electric field due to \( C \) will point away from \( C \), also in the negative \( x \)-direction.
   \[
   E_C = \frac{\sigma_C}{2\epsilon_0} = \frac{6.00 \times 10^{-9}}{2 \times 8.854 \times 10^{-12}} = +338.82 \, \text{N/C}
   \]

3. **Resultant Electric Field:**
   Since both fields are in the same direction (toward the negative \( x \)-axis), we can sum them up:

   \[
   E_{total} = E_B + E_C = -225.88 \, \text{N/C} + 338.82 \, \text{N/C} = +112.94 \, \text{N/C}
   \]

The magnitude of the resultant electric field is approximately \( 112.94 \, \text{N/C} \), and it points in the **positive \( x \)-direction**.

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Would you like further details or have any questions?

Here are 5 relative questions to expand on this:
1. How do surface charge densities of sheets impact electric field direction?
2. How would the result change if the point was located between \( A \) and \( B \)?
3. What would happen if all sheets had the same charge density?
4. Can this principle be extended to non-infinite sheets, and how?
5. How does the permittivity of free space \( \epsilon_0 \) affect the electric field?

**Tip:** The direction of the electric field is always determined by the nature of the charge (positive charges create fields pointing outward, negative charges inward).

What are the magnitude and direction of the resultant electric field at a point that is midway between sheets B and C, or 2.00 cm from each of these two sheets?

Find the magnitude and direction of the electric field at a point midway between two charged sheets. Learn how to calculate using surface charge densities and the superposition principle, suitable for Grades 11-12 physics students.

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