The volume charge density as a function of distance x from one face inside a unit cube varies as shown in the figure. If ρ₀ = 8.85 × 10⁻¹² C m⁻³ and the total electric flux through the cube is n/4 in SI units, find n.

Question

G1 Physics · Accepted Answer

Step 1: By Gauss's law, total flux through the cube is Q/ε₀. The enclosed charge equals the area under the ρ-versus-x graph because the cross-sectional area is 1 m². Step 2: The graph consists of a central rectangle plus two equal triangles: effective width = 1/2 + 2(1/2×1/4)= 3 4 \frac{3}{4} 4 3 ​ . Hence Q=( 3 4 \frac{3}{4} 4 3 ​ )ρ₀. Step 3: Φ=Q/ε₀=( 3 4 \frac{3}{4} 4 3 ​ )(ρ₀/ε₀)= 3 4 \frac{3}{4} 4 3 ​ , so n=3.