Question

going over a couple questions see attachment

Answer 1

The answer to the first question is related to the last answer I gave you. Changing where the zero point is doesn't actually do anything, because the gradient is all that matters.

Answer 2

ok i thought so too

Answer 3

2nd one i thought b and d but that was wrong

Answer 4

The monopole term vanishes if the total charge of the arrangement is zero. That immediately eliminates B,C, and D.

The dipole term survives if the total charge is zero *but* the positives and negatives are still grouped together, forming two electric poles. Hence, dipole. This is the case for A and also for E.

Answer 5

wait a second, but how is the total charge of the arrangement zero for B

Answer 6

Everything is positive.

Answer 7

It's NOT zero which is the point.

Answer 8

If the total charge is nonzero, then the monopole term survives, so the dipole term won't be the first nonzero term.

Answer 9

oh there is no dipole term from monopoles, i see lol

Answer 10

Yup. It goes monopole, dipole, quadrupole, octupole, etc.

Answer 11

multipole expansions always decrease the higher pole right

Answer 12

as the v ~ 1/(r^n) for npole

Answer 13

The potential goes like 1/r for a monopole, 1/r^2 for a dipole, 1/r^3 for a quadrupole, etc.

Answer 14

yeah

Answer 15

i wonder what 16 pole looks like

Answer 16

just what you'd think -- it's the next logical step after the octupole.

Answer 17

Like a flower with sixteen petals.