Three point charges are situated on the z-axis: charge +q is located at z=a, cha

Question

Three point charges are situated on the z-axis: charge +q is located at z=a, charge +2q is located at z = 0, and charge -3q is located at z = -a. Show, in two different ways, that this charge distribution is the same as two physical dipoles (equal and opposite charges separated by some distance). What is the total dipole moment p (magnitude and direction)? Calculate the multipole expansion for the potential V(r) in spherical coordinates (relative to the origin), up to and including terms that vary as 1/r^4. Which, if any, of the multipole terms would change if the charge +2q at. the origin was changed to -2q?

Explanation / Answer

) if we split the charge at z=0 into a -q and a +3q charge then the distribution acts like 2 dipoles

dipole 1 : + q at z=a and -q at z= 0 with centre at a/2 and dipole moment= qa towards z=a

dipole 2 : + 3q at z=0 and - 3q at z= -a with centre at -a/2 and dipole moment= 3qa towards z=0

distance between midpoints of dipole 1 and dipole 2 = a

b) total dipole moment = 3qa + qa = 4qa since both the dipoles are in same direction

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.