Electric Dipole | Definition, Examples, Diagrams
A small electric dipole having dipole moment
p
is placed along X-axis, as shown in the figure. A semi-infinite uniformly charged di-electric thin rod placed along x axis, with one end coinciding with origin. If linear charge density rod is
+
λ
and distance of dipole from rod is
′
a
′
, then calculate the electric force acting on dipole.
Electric field at A due to dipole,
E
A
=
r
3
2
K
P
where
K
=
4
π
ϵ
o
1
E
A
=
(
x
+
a
)
3
2
K
P
Force at A due to dipole,
F
A
=
q
E
A
=
(
λ
d
x
)
×
(
x
+
a
)
3
2
K
P
F
A
=
(
x
+
a
)
3
2
λ
K
P
d
x
Total force exerted due to dipole on the rod,
F
D
=
∫
0
∞
(
x
+
a
)
3
2
λ
K
P
d
x
F
D
=
2
λ
K
P
×
−
2
(
x
+
a
)
2
1
∣
∣
∣
∣
∣
0
∞
⟹
F
D
=
a
2
λ
K
P
Now force exerted by rod on dipole is equal and opposite to
F
D
(Newton’s law)
F
R
=
−
F
D
=
4
π
ϵ
o
a
2
−
λ
P
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