Unformatted text preview: ∇ 2 V ( r, θ ) = 0. (30 points) b) What are the Frst three multipole moments? (30 points) c) What is the leading term in the expansion of the potential for large r ? (20 points) (3) A point dipole v p = p h z is embedded at the center of a sphere of linear dielectric material with radius R and dielectric constant ǫ r . a) The general form of the potential V ( r, θ ), both inside and outside the sphere can be guessed, up to dimensionless constants, using dimensional analysis, the presence of the dipole source and the fact that ∇ 2 V ( r, θ ) = ǫ r ǫ vp · v ∇ δ 3 ( v r ). What is this form? (30 points) b) What are the boundary conditions which apply at the edge of the sphere? (30 points) c) What is V ( r, θ ) both inside and outside the sphere? (20 points)...
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 Spring '08
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 Magnetism, Laplace, Fundamental physics concepts, Leibowitz

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