Three charged cylindrical sheets are present in three spaces with σ = 5 at R = 2m, σ = -2 at R = 4m and σ = -3 at R = 5m. Find the flux density at R = 1m.

To find the electric flux density (D) at (R = 1m) for the given system of charged cylindrical sheets, we must understand a fundamental concept in electromagnetism. The electric flux density (D) outside a charged cylindrical sheet is determined by the total charge enclosed per unit length divided by (2piepsilon_0), where (epsilon_0) is the vacuum permittivity. Inside the cylindrical sheet or in regions where there is no charge enclosed, the electric flux density due to those charges is zero.

Given:

1. A cylindrical sheet with surface charge density (sigma = 5 , text{C/m}^2) at (R = 2m).
2. A cylindrical sheet with surface charge density (sigma = -2 , text{C/m}^2) at (R = 4m).
3. A cylindrical sheet with surface charge density (sigma = -3 , text{C/m}^2) at (R = 5m).

To find the electric flux density (D) at (R = 1m), we only need to consider the fields generated by charges on the inside surface of our point of interest, which is (R =1m) in this case. Since this point is inside all given cylindrical sheets, none of the sheets contribute to the electric flux density at (R = 1m).

Therefore, the answer