Charge of uniform surface density (4.0 nC/m²)is distributed on a spherical surface (radius = 2.0 cm).What is the total electric flux through a concentric spherical surface with a radius of 4.0 cm?

Question

Quizplus · Accepted Answer

The total electric flux through a spherical surface is given by Φ = Q/ε₀ where Q is the total charge enclosed by the surface and ε₀ is the electric constant. In this case, the enclosed charge is the product of the surface charge density (σ) and the surface area of the spherical shell between the two surfaces (4πr²). Therefore, the enclosed charge is Q = σ(4πr²) = (4.0 nC/m²)(4π(0.04 m)²) = 1.024 nC. The electric flux through the larger surface is then Φ = Q/ε₀A = (1.024 nC)/(8.85×10⁻¹² C²/N⋅m²)(4π(0.04 m)²) = 2.28×10⁹ N⋅m²/C = 2.3 N⋅m²/C (or 2.3 V⋅m). Therefore, choice C is the correct answer.

Charge of Uniform Surface Density (4