Electrostatics 7 Question 14
14. Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(d, 0)$ respectively of a $x-y$ co-ordinate system. Then
(1995, 2M)
(a) the electric field $E$ at all points on the $x$-axis has the same direction.
(b) work has to be done in bringing a test charge from $\infty$ to the origin.
(c) electric field at all point on $y$-axis is along $x$-axis.
(d) the dipole moment is $2 q d$ along the $x$-axis.
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Solution:
- The diagramatic representation of the given question is shown in figure.
The electrical field $\mathbf{E}$ at all points on the $x$-axis will not have the same direction.
For $-d \leq x \leq d$, electric field is along positive $x$-axis while for all other points it is along negative $x$-axis.
The electric field $\mathbf{E}$ at all points on the $y$-axis will be parallel to the $x$-axis (i.e. $\hat{\mathbf{i}}$ )
[option (c)]
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 to the origin.
Dipole moment is directed from the $-q$ charge to the $+q$ charge (i.e. $\hat{\mathbf{i}}$ direction).
