Multipole Expansion A sphere of radius R, centered at the origin, carries a charge density R p(r,0) = k÷(R – 2r) sin 0, where k is a constant, and r, 0 are the usual spherical coordinates. To find the approximate potential or r >> R far from the sphere, you will use multipole expnasion. Calculate the potential up to the quadrupole term. Hint: sin? Od0 = n/2 and fo sin* Od0 = 37/8.
Multipole Expansion A sphere of radius R, centered at the origin, carries a charge density R p(r,0) = k÷(R – 2r) sin 0, where k is a constant, and r, 0 are the usual spherical coordinates. To find the approximate potential or r >> R far from the sphere, you will use multipole expnasion. Calculate the potential up to the quadrupole term. Hint: sin? Od0 = n/2 and fo sin* Od0 = 37/8.
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Transcribed Image Text:Multipole Expansion
A sphere of radius R, centered at the origin, carries a charge density
R
p(r, 0) = k(R – 2r) sin 6,
where k is a constant, and r, 0 are the usual spherical coordinates. To find the approximate potential
for r >> R far from the sphere, you will use multipole expnasion. Calculate the potential up to the
quadrupole term.
Hint: sin? Od0 = r/2 and sin“ Od0 = 37/8.
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