Four point charges of magnitude sit in the plane at the corners of a rectangle of…
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Electricity, Magnetism & Electromagnetism · Electrostatic fields and potential
The Boundary-Value Problem, Ch The multipole expansion of the potential
Problem
Four point charges of magnitude q=3.0nC sit in the z=0 plane at the corners of a rectangle of half-widths a=2.0cm and b=3.0cm, with signs alternating around the rectangle: +q at (a,b,0), −q at (−a,b,0), +q at (−a,−b,0), −q at (a,−b,0).
((a)) Show that the total charge and the dipole moment about the origin both vanish.
((b)) Compute every independent component of the traceless quadrupole moment tensor Qij about the origin, and verify explicitly that its trace vanishes.
((c)) State the leading non-vanishing term of the multipole expansion for this arrangement and how its potential falls with distance r.