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Texts: 2. Multipole moments Given a charge distribution ρ = q(r-a) + q(r+a) - q(r-a), where q > 0, R and a are given in Cartesian coordinates by a = a₀₀ and a = 0a₀ with a > 0.

  1. Calculate the resulting potential and the electric field E.
  2. What is the electrostatic energy of this charge distribution (without including the self-energy contribution of the point charges themselves)?
  3. Determine the dipole moment p = ∫dV and the quadrupole moment Q = ∫(3x'x' - r²F) for all i, j = 1, 2, and 3, where F = x'²x'³ = x'²³ and the integrals can be taken to be over the whole of space.
  4. By using the multipole expansion for the potential r up to the quadrupole moment which we derived in the lectures, determine the leading-order behavior of the potential in the following cases:
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Question Text
Texts: 2. Multipole moments Given a charge distribution ρ = q(r-a) + q(r+a) - q(r-a), where q > 0, R and a are given in Cartesian coordinates by a = a₀₀ and a = 0a₀ with a > 0.
TopicAll topics
SubjectPhysics
ClassClass 11