Q. Two point charges $+ q$ and $- q$ are held fixed at $( - d,0)$ and $(d,0)$ respectively of a $(X,Y)$ coordinate system. Then
A) $E$ at all points on the $Y -$ axis is along $\widehat{\mathbf{i}}$
B) The electric field $\overrightarrow{E}$ at all points on the $X$-axis has the same direction
C) Dipole moment is $2qd$ directed along $\widehat{\mathbf{i}}$
D) Work has to be done in bringing a test charge from infinity to the origin
Explanation
(a) From figure, it is clear that $\overrightarrow{E}$ at all points on the $y$-axis is along $\widehat{i}.$ Here $\overrightarrow{E}$ of all points on $x$-axis cannot have the same direction
Here electric potential at origin is zero so no work is done in bringing a test charge from infinity to origin.
Here dipole moment is in $- x$ direction $( - q\ to + q)$
Hence only option (a) is correct
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.