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A solid ball of radius R has a charge density ρ given by ρ = ρ₀ (1 − r/R) for 0 ≤ r ≤ R. The electric field outside the ball is -

1. ρ₀R³/(ε₀r²)
2. 4ρ₀R³/(3ε₀r²)
3. 3ρ₀R³/(4ε₀r²)
4. ρ₀R³/(12ε₀r²)

Correct answer: ρ₀R³/(12ε₀r²)

Solution

The correct option is derived from applying Gauss's law to the charge distribution of the solid ball. The charge density decreases linearly with radius, leading to a total charge that can be calculated and results in the electric field outside the ball being proportional to the total charge divided by the square of the distance from the center, yielding the specific form of the electric field as ρ₀R³/(12ε₀r²).

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