A uniform linear charge density of 4.0 nC/m is distributed along the entire x axis. Consider a spherical (radius = 5.0 cm) surface centered on the origin. Determine the electric flux through this surface. A) 68 N ⋅ m²/C B) 62 N ⋅ m²/C C) 45 N ⋅ m²/C D) 79 N ⋅ m²/C E) 23 N ⋅ m²/C

Question

Quizplus · Accepted Answer

According to Gauss's law, the electric flux through a closed surface is equal to the charge enclosed by the surface divided by the permittivity of free space ($\epsilon_0$). Since the spherical surface does not enclose any part of the linear charge distribution (which lies entirely on the x-axis and the sphere is centered on the origin), the enclosed charge is zero. Therefore, the electric flux through the spherical surface is also zero. However, none of the provided options exactly matches this explanation (zero flux), indicating a possible misunderstanding or error in the question or answer choices. The closest to a correct conceptual answer based on Gauss's law would be to recognize that the actual flux should be zero, but given the options and the context, a more detailed calculation or clarification might be needed to align with the provided choices.

A Uniform Linear Charge Density of 4