When a cube is inscribed in a sphere of radius r, the length L of a side of the cube is . If a positive point charge Q is placed at the center of the spherical surface, the ratio of the electric flux Φ_sphere at the spherical surface to the flux Φ_cube at the surface of the cube is A) . B) . C) 1. D) . E) .

Question

Quizplus · Accepted Answer

The electric flux through a closed surface is given by the equation: Φ = Q/ε0 where Q is the charge enclosed by the surface and ε0 is the permittivity of free space. In this problem, the charge, Q, is placed at the center of the spherical surface, so the electric flux through the spherical surface is given by: Φ_sphere = Q/ε0 For the cube, it is inscribed inside the sphere, so the charge is also enclosed by the cube surface. Thus, the electric flux through the surface of the cube is also given by: Φ_cube = Q/ε0 Therefore, the ratio of the electric fluxes is: Φ_sphere / Φ_cube = (Q/ε0) / (Q/ε0) = 1 Therefore, the correct answer is C.

When a Cube Is Inscribed in a Sphere of Radius