Question

Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(d, 0)$ respectively of a $x-v$ co-ordinate system. Then

• 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 ony-axis is along x-axis
• D. the dipole moment is 2qd along the x-axis

Answer 1

Answer: (C)

The diagramatic representation of the given question is shown in figure.
The electrical field Eat all points on the x-axis will not have the same direction.
For $-d \le x \le d, $ electric field is along positive x-axis while for all other points it is along negative $x$-axis.
The electric field Eat all points on the /-axis will be parallel to the $x$-axis (i.e. $\hat{i}$) [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. $- \hat{i}$ direction).