There are 3 charges: +q, -2q, and +q on the z axis, with -2g at the origin, and +q at z = a and z = -a as shown in the figure below. This system can be considered as a linear quadrupole, oriented along z axis, because the total charge is zero and the dipole moment is zero (consider it as two dipoles (+q, -q) pointing in opposite directions). Using the principle of superposition, the exact electric potential of this quadrupole is written as: V (r, 0) Vr? +a²–2arcose V ta²+2arcos0 Find the approximate electric potential of this quadrupole at the large distance r from it. -29 +q

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There are 3 charges: +q, -2q, and +q on the z axis, with -2q at the origin,
and +q at z = a and z = -a as shown in the figure below. This system can be
considered as a linear quadrupole, oriented along z axis, because the total
charge is zero and the dipole moment is zero (consider it as two dipoles
(+q, -q) pointing in opposite directions). Using the principle of
superposition, the exact electric potential of this quadrupole is written as:
V (r, 0) = {
%3D
4T€o Vr2 +a? -2arcose
Vr? +a?+2arcos0
Find the approximate electric potential of this quadrupole at the large
distance r from it.
-29
+q
Transcribed Image Text:There are 3 charges: +q, -2q, and +q on the z axis, with -2q at the origin, and +q at z = a and z = -a as shown in the figure below. This system can be considered as a linear quadrupole, oriented along z axis, because the total charge is zero and the dipole moment is zero (consider it as two dipoles (+q, -q) pointing in opposite directions). Using the principle of superposition, the exact electric potential of this quadrupole is written as: V (r, 0) = { %3D 4T€o Vr2 +a? -2arcose Vr? +a?+2arcos0 Find the approximate electric potential of this quadrupole at the large distance r from it. -29 +q
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