- #1
ToothandnaiL
- 6
- 0
So we're currently covering multipole expansion techniques in my EDM class. The multipole expansion is a summation of integrals each treating a different configuration of discrete charges (monopole, dipole... and so on). The term in the summation that corresponds to the physical configuration that your dealing with, whether it be a monopole, dipole, or whatever, is the dominant term. My first question is: Does that mean it is safe to ignore the other terms in the summation and treat, say, a quadrupole with only the quadrupole term? Secondly, there is a simple formula to express the potential of a discrete charge configuration at a large distance where the configuration appears as a single point charge. The problem I'm looking at has a charge configuration like this: a +3q charge at point z=a, a +q charge at z=-a, a -2q charge at y=a and y=-a, this forms a quadrupole and the problem wants an expression for potential that is valid at large distances from the quadrupole. It uses the word 'simple' to describe the expression for potential so I imagine it's not the multipole expansion formula. Would I use the formula for large distances to treat this problem? The only problem I see with that would be the fact that the net charge would=0 and then the potential would= 0 as well. How could that be the case for this quadrupole?