A uniform charge density of 500 nC/m³ is distributed throughout a spherical volume (radius = 16 cm). Consider a cubical (4.0 cm along the edge) surface completely inside the sphere. Determine the electric flux through this surface. A) 7.1 N ⋅ m²/C B) 3.6 N ⋅ m²/C C) 12 N ⋅ m²/C D) 19 N ⋅ m²/C E) 970 N ⋅ m²/C

Question

Quizplus · Accepted Answer

To use Gauss's law, we need to find a closed Gaussian surface that encloses the same charge as the given cubical surface. Since the charge distribution is spherically symmetric, we can choose a spherical Gaussian surface with radius 16 cm. The electric flux through this spherical surface is given by:

Φ = Q / ε0

where Q is the total charge enclosed by the Gaussian surface and ε0 is the permittivity of free space. The total charge enclosed by the Gaussian surface is:

Q = ρ * V

where ρ is the charge density and V is the volume of the Gaussian sphere. The volume of a sphere is given by:

V = (4/3) * π * r^3

where r is the radius of the sphere. Substituting the given values, we get:

V = (4/3) * π * (16 cm)^3 = 17,069 cm^3

and

Q = (500 nC/m^3) * (17,069 cm^3) * (10^-9 C/nC) = 8.534 C

Substituting these values into the equation for electric flux, we get:

Φ = Q / ε0 = (8.534 C) / (8.85 x 10^-12 N^-1 m^-2 C^2) = 3.63 x 10^11 N m^2 C^-1 ≈ 3.6 N⋅m2C−1

Therefore, the answer is B.

A Uniform Charge Density of 500 NC/m3 Is Distributed Throughout

A Uniform Charge Density of 500 NC/m³ Is Distributed Throughout