A report states: "the dipole moment of a ion is "

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electrostatic fields and potential · Electrostatic fields and potential

The Boundary-Value Problem, Ch The multipole expansion of the potential

Problem

A report states: "the dipole moment of a +2e+2e ion is p=4.8×10−29 C mp=4.8\times10^{-29}\,\mathrm{C\,m}", with no origin specified, and treats this number as an intrinsic property of the ion, usable in any calculation regardless of where the origin is placed. Take e=1.602×10−19 Ce=1.602\times10^{-19}\,\mathrm{C}. ((a)) Find the error in treating this number as origin-independent, and find the distance bb from the quoted origin, measured along the dipole direction, at which the ion's dipole moment about that new origin is exactly zero. ((b)) Find the ion's dipole moment about an origin that lies 0.050 nm0.050\,\mathrm{nm} from the original one, displaced along the same direction as p\mathbf p (towards the point found in part (a)).

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