A charge q is placed inside a sphere of radius \"a\" filled with wa...

Question

A charge q is placed inside a sphere of radius \"a\" filled with water and another charge 2q is placed inside a cube of side \"2a\" which is vacuumed inside. Find the ratio of the flux linked with the sphere to that linked with the cube. (Take relative permittivity of water as 80)

Accepted Answer

Given:
• Sphere: charge q, medium = water, K = 80
• Cube: charge 2q, medium = vacuum, K = 1

Concept:
In a medium of dielectric constant K, Gauss\'s law becomes:
φ = q_enclosed/(K·ε₀)

Step 1: Flux through sphere (in water)
φ_sphere = q/(K · ε₀)
φ_sphere = q/(80 · ε₀)

Step 2: Flux through cube (in vacuum)
φ_cube = 2q/ε₀

Step 3: Calculate ratio
φ_sphere/φ_cube = [q/(80·ε₀)] ÷ [2q/ε₀]

φ_sphere/φ_cube = q/(80·ε₀) × ε₀/(2q)

φ_sphere/φ_cube = 1/160

Answer:
φ_sphere : φ_cube = 1 : 160

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