Two point charges +8 μC and -2 μC are located on the x-axis at x = 2 cm and x = 4 cm, respectively. Two Gaussian spheres are centred at the origin and have radii 3 cm and 5 cm. What is the ratio of the electric flux through the 3 cm sphere to that through the 5 cm sphere?
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Question

Two point charges +8 μC and -2 μC are located on the x-axis at x = 2 cm and x = 4 cm, respectively. Two Gaussian spheres are centred at the origin and have radii 3 cm and 5 cm. What is the ratio of the electric flux through the 3 cm sphere to that through the 5 cm sphere?

Options

G1 Physics · Accepted Answer

By Gauss's law, Φ = Q(enclosed) ÷ ε₀. The 3 cm sphere encloses only the charge at x = 2 cm: Q₁ = +8 μC. Therefore, Φ₁ = 8 μC ÷ ε₀. The 5 cm sphere encloses both charges: Q₂ = 8 μC-2 μC = 6 μC. Thus, Φ₂ = 6 μC ÷ ε₀. Hence, Φ₁:Φ₂ = 8:6 = 4:3. Correct option: C.