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Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(+d, 0)$ respectively of a $(x, y)$ coordinate system. Then
$E$ at all points on the $y-axis$ is along $\hat i$
The electric field $\overrightarrow E$ at all points on the $x-axis$ has the direction along $\hat i$
Dipole moment is $2qd$ directed along $\hat i$
Work has to be done in bringing a test charge from infinity to the origin
Solution
The diagrammatic representation of the given question is shown in figure.
The electrical field vector $E$ at all points on the $x$ $-axis$ will not have the same direction.
For $-\mathrm{d} \leq \mathrm{x} \leq \mathrm{d},$ electric field is along positive $\mathrm{x}$ $-axis$ while for all other points it is along negative $x-axis.$ The electric field vector $E$ at all points on the $y$ $-axis$ will be parallel to the $x$ $-axis$ (i.e.,i)
The electrical potential at the origin due to both the charges is zero, hence no work is done in bringing a test charge from infinity of the origin.
Dipole moment is directed from the $-q$ charge to the $+ q$ charge $(i.e.,- i direction)$
