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Charge in the form of a plane sheet with density ρs = 40 μC/m2 is located at z = -0.5 m. A uniform line charge of ρl = -6 μC/m lies along the y axis. What net flux crosses the surface of a cube 2 m on an edge, centered at the origin?

Charge in the form of a plane sheet with density ρs = 40 μC/m2 is located at z = -0.5 m. A uniform line charge of ρl = -6 μC/m lies along the y axis. What net flux crosses the surface of a cube 2 m on an edge, centered at the origin? Correct Answer 148 μC

Qenc = ∫ρsds

Qnet = Qsurface + Qline 

ρs = 40 μ c/m2

ρℓ = -6μ c/m

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Now, the area of the cube is where the sheet lies = 2 × 2 = 4m2

Qsurface = 40 × 4 = 160 μC

Now, for Qline

Qline = ∫ρℓdl

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= ∫(-6) × (2) = -12 μC

∴ Qnet = 160 – 12 = 148 μC

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