A long linear charge distribution of uniform 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 a closed surface is given by the formula:
Φ = q/ε0
where q is the net charge enclosed by the surface and ε0 is the permittivity of free space.

In this problem, the cylinder is concentric with the long linear charge distribution, so all of the charge in the distribution is enclosed by the cylinder. Therefore, the net charge enclosed by the cylinder is equal to the total charge in the distribution.

The total charge in the distribution is given by:
Q = λL
where λ is the charge density (1.35 nC/m) and L is the length of the distribution (not given in the problem).

The length of the distribution is not given, but it is not needed to solve the problem. The electric flux through the cylinder only depends on the total charge enclosed by the cylinder, which is the same regardless of the length of the distribution.

The radius of the cylinder is given as 23.6 cm = 0.236 m. The circumference of the cylinder is:
C = 2πr = 2π(0.236 m) = 1.48 m

Therefore, the electric flux through the cylinder is:
Φ = Q/ε0 = λLC/ε0 = (1.35×10^-9 C/m)(1.60 m)(1.48 m)/8.85×10^-12 C^2/(N·m^2)
Φ ≈ 244 N·m^2/C

The correct answer is choice C.

A Long Linear Charge Distribution of Uniform Charge Density 1