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

Answer: (B)

As shown in figure, charge $-2q$ is at $O(0,0,0),+q$
is at $A(0,a,0)$ and $+q$ is at $B(a,0,0)$.
The given arrangement of charges consists of two dipoles $-q$ and $+q$ with dipole moment ${\vec{p}}_1$ along $+y$ direction and $-q$ and $+q$ with dipole moment ${\vec{p}}_2$ along $+x$ direction
i.e., $P_1=qa$ along $OA$
$P_2=qa$ along $OB$
Resultant dipole moment $\vec{p}$ is along $OC$ where $(C=a,a,0)$
$P=\sqrt{P_1^2+P_2^2}$
$=\sqrt{{\left(qa\right)}^2+{\left(qa\right)}^2}$
$=\sqrt{2}qa$