Two parallel large thin metal sheets have equal surface charge densities `(sigma = 26.4 xx 10^(-12) C//m^(2))` of opposite signs. The electric field between these sheets is

Options

A. `3 N//C`
B. `1.5 xx 10^(-10) N//C`
C. `1.5 N//C`
D. `3 xx 10^(-10) N//C`

Explanation

To find the electric field between two parallel large thin metal sheets with equal surface charge densities of opposite signs, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Surface Charge Densities**:
Let the surface charge density on the positively charged plate be \( \sigma = 26.4 \times 10^{-12} \, \text{C/m}^2 \) and on the negatively charged plate be \( -\sigma = -26.4 \times 10^{-12} \, \text{C/m}^2 \).

2. **Understand the Electric Field Due to a Single Plate**:
The electric field \( E \) due to a single infinite plane sheet of charge with surface charge density \( \sigma \) is given by the formula:
\[ E = \frac{\sigma}{2\epsilon_0} \]
where \( \epsilon_0 \) is the permittivity of free space, approximately \( 8.85 \times 10^{-12} \, \text{C}^2/\text{N m}^2 \).

3. **Calculate the Electric Field from Each Plate**:
- For the positively charged plate:
\[ E_1 = \frac{\sigma}{2\epsilon_0} \]
- For the negatively charged plate:
\[ E_2 = \frac{-\sigma}{2\epsilon_0} \]
However, since the electric field direction due to the negative plate is opposite to that of the positive plate, we will consider the magnitudes when calculating the total electric field between the plates.

4. **Determine the Total Electric Field Between the Plates**:
The total electric field \( E \) between the plates is the sum of the electric fields due to both plates:
\[ E = E_1 + |E_2| = \frac{\sigma}{2\epsilon_0} + \frac{\sigma}{2\epsilon_0} = \frac{\sigma}{\epsilon_0} \]

5. **Substitute the Values**:
Now we can substitute the values of \( \sigma \) and \( \epsilon_0 \):
\[ E = \frac{26.4 \times 10^{-12}}{8.85 \times 10^{-12}} \, \text{N/C} \]

6. **Calculate the Result**:
Performing the calculation:
\[ E \approx \frac{26.4}{8.85} \times 10^{0} \, \text{N/C} \approx 2.98 \, \text{N/C} \]

### Final Answer:
The electric field between the two parallel sheets is approximately \( 2.98 \, \text{N/C} \).

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