Electric Field Flux Calculation and Line Charge Density

What is the line charge density of the line charge if the electric field flux through a cylinder surrounding a section of the line charge is 162,317 N*m²/c? The line charge density of the line charge can be calculated using Gauss's Law. According to Gauss's law, the electric flux passing through a closed surface is equal to the charge enclosed by the surface divided by the permittivity of free space. The electric flux φ is given as 162,317 N*m²/C. Therefore, the enclosed charge q can be found by multiplying φ by the permittivity of free space (ε0=8.85*10^-12 C²/N*m²), which yields approximately 1.436 µC. Given the length of the section surrounded by the cylinder as mentioned in the question is 0.4 m, the linear charge density λ can thus be calculated as q/0.4 m = 3.59 µC/m.

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.

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