Electromagnetism - Quadrupole , Octupole

[syracuse1234]

1.Calculate the electric field of a quadrupole in spherical coordinates.

2.Calculate the electric field of a octupole in spherical coordinates.

 

[Troels]

There seems to be missing some information here. How exactly are those multi-poles arranged? equal charges? equal distances? Regular polygons? "a quadupole" or "an octopole" are very wide terms indeed

 

[Meir Achuz]

1.Calculate the electric field of a quadrupole in spherical coordinates.

2.Calculate the electric field of a octupole in spherical coordinates.

Use the multipole expansion for the potential in terms of Legendre polynomials for the case of an axially symmetric chargel distribution. If itr is not axially slymmetric, you need the spherical harmonic expansion.

 

[sci.chris]

Also see Boas (Math Methods) Ch. 12 sect.5 ex. 1 for future reference. Solution if You have 2 +ve charges Q at +/- "a" on y-axis and 2 -ve charges Q at +/- "a" on x-axis is $$V=\frac{-3Qa^{2}cos(2\theta)}{4\pi\epsilon_{0}r^{3}}$$