Multipole expansion
3 important questions on Multipole expansion
What happens if total charge si zero? What is a physical dipole and what is a perfect dipole?
The dominant term in the potewntial will be the dipole unless it vanishes. This is represented by a dipo;e moment of a distribution. A physical dipole has equal and oppsoutwe charge. Where d is a vector from the netaive charge to the positive charge. To construct a perfect dipole, yud have to let d approach zero.
What happens when a point charge is not at the origin?
It is then not a pure monpole. When this si the case the monopole moment does not change since total charge is oobviously independent of coordinate system,, however the dipole moment does change wgen you shift the origin. However wgen the total charge is zerie han the dipole moment is independent of the choice of origin.
The electric field of a dipole
monopole inverse square 1/r^2 . Thus dipopel is It is indicated by 1/r^3 . Thus quadrupole is 1/r^4 octpole is 1/r^5. The electric fields of a pure dipole and a physical dipole if you zoom out will b eentirely diffferent so you need to have r>>d
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