The Flux Density at the Boundary

To find the flux density at the boundary, we need to understand the concept of flux and how it relates to charge density.

1. What is Flux?
Flux is a measure of the flow of a physical quantity through a given surface. In the context of electromagnetism, flux refers to the flow of electric field lines through a surface.

2. What is Flux Density?
Flux density, also known as electric flux density or electric displacement, is a measure of the electric field strength per unit area. It is given by the formula:
D = εE
where D is the electric flux density, ε is the permittivity of the medium, and E is the electric field strength.

3. Relationship between Flux and Charge Density
The flux passing through a closed surface is directly proportional to the charge enclosed by that surface. Mathematically, this relationship can be expressed as:
Φ = Q/ε
where Φ is the flux, Q is the charge enclosed, and ε is the permittivity of the medium.

4. Calculating Flux Density at the Boundary
In this problem, the charge density is given as 24 units. We need to find the flux density at the boundary, which means we need to calculate the flux passing through the boundary surface.

Since the charge density is constant, we can assume that the charge is uniformly distributed over the surface. Therefore, the charge enclosed by the boundary surface is given by:
Q = Charge density × Area

Let's assume the area of the boundary surface is A. Then, the charge enclosed is:
Q = 24 × A

Using the relationship between flux and charge density, we can calculate the flux passing through the boundary surface as:
Φ = Q/ε
= (24 × A) / ε

Finally, to find the flux density, we divide the flux by the area of the boundary surface:
D = Φ / A
= (24 × A) / (ε × A)
= 24 / ε

The value of ε depends on the medium between the charges. Without information about the medium, we cannot determine the exact value of ε. However, regardless of the value of ε, the flux density D will be constant at 24 units.

Conclusion
The correct answer is option 'B' (24). The flux density at the boundary is independent of the charge density and is solely determined by the properties of the medium.