A charged rod-like assembly of overall size carries a non-zero net charge (so its…

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 charged rod-like assembly of overall size a=1.0 cma=1.0\,\mathrm{cm} carries a non-zero net charge (so its leading moment is the monopole, ℓ0=0\ell_0=0) and is viewed from a distance r=50 cmr=50\,\mathrm{cm}. Use the truncation rule that stopping after order LL leaves a fractional error of about (a/r)L+1−ℓ0(a/r)^{L+1-\ell_0} relative to the leading (monopole) term. ((a)) Estimate the fractional error made by keeping the monopole term alone (L=0L=0). ((b)) Find the smallest LL for which the fractional error falls below 0.1%0.1\%, and state the resulting error.

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