W9_parallel_resonance.eps

Week 1: Discrete Charge and the Electrostatic Field 53

Problem 2.

y

x

−a

+a

x

Two equal positive charges +qsit aty=−aandy= +a.

a) Find the electric field at an arbitrary point on thexaxis, and find its asymptotic form when

x≪a(near the origin) andx≫a(far from the pair of charges). Explain the latter result

intuitively.

b) Repeat for a positive charge +qaty= +aand a negative charge−qaty=−a.

c) Repeat for two equal positive charges +qsitting aty=−aandy= +a, and athirdcharge

of− 2 qat the origin. Note that in this arrangement, the net charge is zero(so we expect no

monopolar field far away). The two visible dipolesalsocancel, so we expect nodipolarfield

far away. What might we call the first surviving term in the distant field? (Note that there

arefourmonopoles in this distribution.)