Question

Three point charges $+q,-2q$ and $+q$ are placed at points $(x=0,y=a,z=0),(x=0,y=0,z=0)$ and $(x=a,y=0,z=0)$ respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are:

• A. $\sqrt{2}qa$ along $+y$ direction
• B. $\sqrt{2}qa$ along the line joining points $(x=0,y=0,z=0)$ and $(x=a,y=a,z=0)$
• C. $qa$ along the line joining points $(x=0,y=0,z=0)$ and $(x=a,y=a,z=0)$
• D. $\sqrt{2}qa$ along $+x$ direction

Answer 1

The correct option is B $\sqrt{2}qa$ along the line joining points $(x=0,y=0,z=0)$ and $(x=a,y=a,z=0)$


Assemble can be treated as combination of 2 dipoles along $X-$ axis and $Y-$ axis repectively with dipole moment $P=qa$ each.
Net dipole moment
$P_{net}=P\hat{i}+P\hat{j}=P\sqrt{2}$
i.e $P_{net}=\sqrt{2}qa$
along the line joining points $(x=0,y=0,z=0)$ and $(x=a,y=a,z=0)$
(using parallelogram law)