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Four point charges -q, +q, +q and -q are placed on y-axis at y = -2d, y = -d, y = +d, y = +2d, respectively. The magnitude of the electric field E at a point on the x-axis at x = D, with D >> d, will behave as:

1. E ∝ 1/D
2. E ∝ 1/D³
3. E ∝ 1/D⁴
4. E ∝ 1/D²

Correct answer: E ∝ 1/D⁴

Solution

Total charge = 0 and dipole moment Sum(q*y) = 0, but the quadrupole moment Sum(q*y^2) = -6qd^2 is nonzero. A quadrupole field falls off as 1/D^4, so E ~ 1/D^4.

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