Answer:
(a) Point (0, 0, z)
lies on the axis of the given dipole.
Potential on a point on the axial
line of dipole,
where
p = q × 2a
Point
(x, y, 0) means normal to the dipole, so the potential is zero.
(b)
Consider P to be the point of observation at a distance r from the centre (O)
of the electric dipole. Let OP make an angle with
the dipole moment and r1,
r2 be the distances of point P from ? q charge and + q charge
respectively.
Potential
at P due to ?q charge,
Potential
at P due to + q charge,
Potential at P due to the dipole.
V
= V1 + V2
Or
Or
Now
draw a perpendicular from A which meets the line OP at C when produced
backward. Also draw
Then,
r1=
(from
)
and
r2 = BP = DP = OP ? OD
(from
)
(dipole
moment, )
If
r > > 1, then
When
the dependence of
the potential on distance is of type.
(c)
Zero
Answer
does not change because in electrostatics, the work done does not depend upon
actual path, it simply depends upon the initial and final positions.
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