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NCERT Class XII Chapter
Electrostatic Potential and Capacitance
Questions With Solutions

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Question : 22
Total: 37
Figure shows a charge array known as an electric quadrupole. For a point on the axis of quadrupole, obtain the dependence of potential on r for r/a >> 1, and contrast your results with that due to an electric dipole, and an electric monopole (i.e., a single charge).
Solution:  
VP = VPA+VPB+VPC+VPD
or VP =
1
4πε0
 [
+q
r+a
−
q
r
−
q
r
+
q
r−a
]
or VP =
q
4πε0
[
r(r−a)−2(r2−a2)+r(r+a)
r(r2−a2)
]

or VP =
q
4πε
 [
r2−ra−2r2+a2+r2+ra
r(r2−a2)
]

or VP =
1
4πε0
q.2a2
r(r2−a2)
 =
1
4πε0
p.a
r(r2−a2)
For
r
a
 ≫ or r ≫ a
VP ~
1
4πε0
pa
r3
 or VP α
1
r3
However, electric potential at any point on axis of electric dipole is
V =
1
4πε0
p
r2
 or V α
1
r2
 and due to point charge is
V =
1
4πε0
q
r
 or V α
1
r
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