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ત્રણ વિદ્યુતભાર $ q,-2q $ અને $q$ અનુક્રમે $(x=0,y=a, z=0) , (x=0,y=0, z=0) $ અને $(x=a,y=0, z=0) $ પર મૂકેલા છે.તો પરિણામી વિદ્યુત ડાઇપોલ મોમેન્ટ
$\sqrt 2 qa\;$$,(x=0,y=0, z=0) $ થી $(x=a,y=a, z=0)$ દિશામાં
$qa\;$$,(x=0,y=0, z=0) $ થી $ (x=a,y=a, z=0)$ દિશામાં
$\sqrt 2 qa\;$$,+x- $ દિશામાં
$\;\sqrt 2 qa\;$$,+y-$દિશામાં
Solution
The given charge assembly can be represented using the three co-ordinate axes $x , y$ and $z$ as shown in figure.
The charge $-2 q$ is placed at the origin $O$. One $+ q$ charge is place at $( a , o , 0)$ and the other $+q$ charge is placed at $(0, a, 0)$. Thus the system has two dipoles along $x$-axis and $y$-axis respectively.
As the electric dipole moment is directed from the negative to the positive charge hence the resultant dipole moment will be along $OA$ where coordinates of point $A$ are $( a , a , o )$. The magnitude of each dipole moment, , $p = qa$
So, the magnitude of resultant dipole moment is
$P _{ R }=\sqrt{ p ^2+ P ^2}=\sqrt{( qa )^2+( qa )^2}=\sqrt{2 qa }$
