Discussion
Three charges lie on a straight line: \( +q \), \( -2q \) and \( +q \), equally spaced. The arrangement is
Answer: C
Correct answer: a linear quadrupole with zero net charge and zero dipole moment
The charges sum to \( q - 2q + q = 0 \), so there is no monopole term, and the two dipole moments formed by the outer charges against the centre are equal and opposite, so the dipole moment vanishes as well. What remains is the next term in the expansion, the quadrupole, and its field falls as \( 1/r^4 \) - faster still than a dipole’s.
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