Prove that the electric intensity at a axial line is twice than the electric intensity placed at a same distance on the equatorial line
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Consider the an electric dipole of charges +q and −q separated by distance 2a with center at O.
Goal: To find electric field at point P on the axial line of the dipole, OP=r.
Let E
1
and E
2
be electric field on P due to charges +q and −q respectively.
E
1
=
(r−a)
2
kq
along AP
E
2
=
(r+a)
2
kq
along BP
The resultant electric field at P, E=E
1
−E
2
(as both E
1
and E
2
are in opposite direction)
E=
(r−a)
2
kq
−
(r+a)
2
kq
=kq
(r
2
−a
2
)
2
4ra
Define, p=2aq
E=k
(r
2
−a
2
)
2
2pr
If r>>a, then E=k
r
4
2pr
=k
r
3
2p
.
In vector form,
E
=k
r
3
2
p
.
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