1) A charge 𝒒𝟏 = +𝟐𝒆 is located at the origin and a charge 𝒒𝟐 = −𝒆 is located at the point (x,y) = (1,0).
a) Evaluate the potential at the points P1 = (0,5) and P2 = (5,0) by a direct calculation for each charge.
b) Find the first three moments of the charge distribution. Calculate the potential at P1 and P2 using these terms of the multipole expansion. Discuss the difference in in the rates of convergence of the expansions for the two field points.
2) The linear charge density on a ring of radius a is given by 𝝆𝒍 = 𝒒(𝐜𝐨𝐬𝝋−𝐬𝐢𝐧𝟐𝝋)
a) Find the monopole, dipole, and quadrupole moments of the system.
b) Use these moments to express the potential at an arbitrary point in space.
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