(a) Three charges are sketched at the corners of an isosceles triangle: at , and at…
PHYSICS · Subjective · 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) Three charges are sketched at the corners of an isosceles triangle: +q at (0,0,d), and −q/2 at each of (d,0,0) and (−d,0,0). Identify the leading non-vanishing multipole moment of this arrangement about the origin, give its value and direction, and state how the corresponding term of the potential varies with the polar angle θ measured from the z axis. (b) A field-line diagram of a small, overall neutral polarised object shows lines leaving densely from its top and curving around to re-enter densely at its bottom; measured at equal distances r from the centre, the field strength directly above the top is about twice the field strength to the side (in the equatorial plane). State the direction of the dipole moment p of the object relative to top and bottom, using the direction of the field on the axis, and say what the factor of two tells you about the object.