Consider a line charge density A(z) that is localized on the z axis from z=-a to z=+a. By considering the monopole, dipole, andquadrapole moments of the charge distribution, find an approximation for the potential p(r) to leading order only (i.e. the first non-vanishing term) in the multipole expansion, for each of the following three cases:a) A(z) Acos(TZ/2a)b) A(z) Aosin(TZ/a)c) MZ) Aocos(Tz/a)

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Asked Oct 8, 2019
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It's an electromagnetics problem.

Consider a line charge density A(z) that is localized on the z axis from z=-a to z=+a. By considering the monopole, dipole, and
quadrapole moments of the charge distribution, find an approximation for the potential p(r) to leading order only (i.e. the first non-
vanishing term) in the multipole expansion, for each of the following three cases:
a) A(z) Acos(TZ/2a)
b) A(z) Aosin(TZ/a)
c) MZ) Aocos(Tz/a)
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Consider a line charge density A(z) that is localized on the z axis from z=-a to z=+a. By considering the monopole, dipole, and quadrapole moments of the charge distribution, find an approximation for the potential p(r) to leading order only (i.e. the first non- vanishing term) in the multipole expansion, for each of the following three cases: a) A(z) Acos(TZ/2a) b) A(z) Aosin(TZ/a) c) MZ) Aocos(Tz/a)

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Step 1

 (a)

Write the expression for the monopole moment

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z-+a Q= 2(2) dz z--a z-+a = j 4,cos| dz 2a 22ga -T - sin sin 2

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Step 2

Substitute the monopole moment in the multipole expansion

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VF) = a V (F) k

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Step 3

(b)

Write the expression for t...

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Z-+a Q= 2(z)dz 22)dz z--a dz A,sin 2a -22a -T - cos 2 cos 0

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