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Given: Length of the dipole (2l) = 10 cm = 0.1 m or l = 0.05 m. Charge on the dipole (q) = 500 μC = 500 × 10^-6 C and distance of the point on the axis from the mid-point of the dipole (r) = 20 + 5 = 25 cm = 0.25 m. We know that the electric field intensity due to dipole on the given point (E) = (1/4πε₀) × (2q(2l)r/(r² - l²)²).

1. 9×10^9 × 2(500×10^-6×0.1)×0.25/[(0.25)² - (0.05)²]²
2. 225×10^3/(3.6×10^-3) = 6.25×10^7 N/C
3. The dipole field E ∝ 1/r³ decreases much rapidly as compared to the field of a point charge E ∝ 1/r².
4. Charge on elementary portion dx = λ dx.

Correct answer: The dipole field E ∝ 1/r³ decreases much rapidly as compared to the field of a point charge E ∝ 1/r².

Solution

Option C is correct because the electric field of a dipole decreases as 1/r³, which is faster than the 1/r² dependence of a point charge's field. This is a fundamental property of dipole fields.

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