Find the flux density at the boundary when the charge density is given by 24 units.

The electric flux density, often symbolized by ( mathbf{D} ), at a boundary due to a charge distribution is directly related to the charge density, which is often denoted by ( rho ) (for volume charge density) or ( sigma ) (for surface charge density), depending on the context of your question. The units of charge density you’ve provided are not fully specified (e.g., ( text{C/m}^3 ) for volume charge density or ( text{C/m}^2 ) for surface charge density), nor is the geometry of the situation (point charge, spherical symmetry, planar boundary, etc.) mentioned. These details significantly affect the calculation of flux density.

However, assuming a simple case where the charge density is a surface charge density ( sigma ) (since you mentioned ‘boundary’), and we are dealing with electrostatic conditions, the relationship between surface charge density and electric flux density can be straightforward. Under electrostatic conditions and in a vacuum or air, the electric displacement field ( mathbf{D} ) is related to the electric field ( mathbf{E} ) by the equation:

[ mathbf{D} = epsilon_0 mathbf{E} ]

And the electric field ( mathbf{E} ) near a surface charge density ( sigma ) can be related by Gauss’s law:

[ sigma =