A long linear charge distribution of charge density 1.35 nC/m is surrounded by a concentric cylindrical surface of length 1.60 m and radius 23.6 cm.What is the electric flux through the surface of the cylinder? A) 0.00 B) 160 N·m²/C C) 244 N·m²/C D) 280 N·m²/C E) 316 N·m²/C

Question

Quizplus · Accepted Answer

The electric flux through the surface of the cylinder can be found using Gauss's law.

The electric flux through the surface is given by:

Φ = E * A

where E is the electric field and A is the surface area of the cylinder.

Using Gauss's law, we can find the electric field at any point outside the charged cylinder:

E = (λ / 2πε₀r)

where λ is the linear charge density, ε₀ is the permittivity of free space, and r is the distance from the charged cylinder.

At the surface of the cylinder, the electric field is perpendicular to the surface, so the flux through the surface is simply:

Φ = E * A = (λ / 2πε₀R) * L

where R is the radius of the cylinder and L is the length of the cylinder.

Substituting the given values, we get:

Φ = (1.35 × 10^-9 C/m) / (2π × 8.85 × 10^-12 C^2 N^-1 m^-2 × 0.236 m) × 1.60 m

Φ ≈ 244 N·m^2·C^-1

Therefore, the answer is C.

A Long Linear Charge Distribution of Charge Density 1