To find the flux density of a sheet of charge density in air, we can use Gauss's Law. Gauss's Law states that the flux passing through a closed surface is equal to the total charge enclosed by that surface divided by the permittivity of the medium. In this case, since the charge is distributed over a sheet, we can consider a rectangular Gaussian surface with one side aligned with the sheet.

Let's go through the solution step by step:

1. Define the problem:
- Charge density of the sheet = 25 units
- We need to find the flux density

2. Determine the Gaussian surface:
- Consider a rectangular Gaussian surface with one side aligned with the sheet. The area vector of this surface will be perpendicular to the sheet.

3. Apply Gauss's Law:
- According to Gauss's Law, the flux (Φ) passing through the Gaussian surface is equal to the charge enclosed (Q) divided by the permittivity of the medium (ε₀).
- Φ = Q / ε₀

4. Calculate the charge enclosed:
- The charge enclosed by the Gaussian surface is equal to the charge density (σ) multiplied by the area (A) of the surface.
- Q = σ * A

5. Calculate the flux:
- Substituting the value of Q in the flux equation, we get:
- Φ = σ * A / ε₀

6. Simplify the equation:
- In air, the permittivity (ε₀) is a constant value.
- Let's assume the area of the Gaussian surface is A.
- The charge density (σ) is given as 25 units.
- Substituting these values, we get:
- Φ = 25 * A / ε₀

7. Determine the flux density:
- The flux density (D) is equal to the flux (Φ) divided by the area (A) of the surface.
- D = Φ / A
- Substituting the value of Φ from the previous step, we get:
- D = (25 * A / ε₀) / A
- D = 25 / ε₀

8. Find the value of ε₀:
- The permittivity of free space (ε₀) is a constant value approximately equal to 8.85 x 10^-12 F/m.

9. Calculate the flux density:
- Substituting the value of ε₀, we get:
- D = 25 / 8.85 x 10^-12
- D ≈ 2.82 x 10^12

10. Convert the flux density to scientific notation:
- D ≈ 2.82 x 10^12 C/m²

Therefore, the flux density of the sheet of charge density 25 units in air is approximately 2.82 x 10^12 C/m².
This value corresponds to option 'B' in the given answer choices.

Bhh