Electric Field Flux Calculation and Line Charge Density
To determine the line charge density of the line charge, we first need to calculate the charge enclosed within the section surrounded by the cylinder. The electric flux passing through the cylinder is given as 162,317 N*m²/C. This electric flux is a measure of the total electric field passing through a closed surface. By applying Gauss's Law, we can relate the electric flux to the charge enclosed within the surface.
The formula for Gauss's Law is: Φ = q/ε0, where Φ represents the electric flux, q is the charge enclosed, and ε0 is the permittivity of free space. Rearranging the formula to solve for q, we get q = Φ * ε0. Substituting the given values, we find q = 162,317 N*m²/C * 8.85*10^-12 C²/N*m² ≈ 1.436 µC.
Next, we use the definition of linear charge density, which is given by the formula λ = q/L, where q is the charge and L is the length of the section. The length of the section surrounded by the cylinder is given as 0.4 m. Substituting the values, we get λ = 1.436 µC / 0.4 m ≈ 3.59 µC/m. Therefore, the line charge density of the line charge in this scenario is approximately 3.59 µC/m.
By understanding Gauss's Law and the concept of electric flux, we are able to calculate the line charge density of the line charge based on the given parameters. This calculation showcases the relationship between electric field flux, charge enclosed, and linear charge density in an infinite line charge scenario surrounded by a right circular cylinder.