question_answer

Three point charges \[+q,-2q\] and \[+q\] are placed at points \[(x=0,y=a,x=0),\]\[(x=0,y=0,z=0)\] 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

Correct Answer: B

Solution :

Key Idea Electric dipole moment is a vector quantity directed from negative charge to the similar positive charge. Choose the three coordinate axes as x, y and i and plot the charges with the given coordinates as shown. \[O\]is the origin at which \[-2q\] charge is placed. The system is equivalent to two dipoles along \[x\] and \[y-\]directions respectively. The dipole moments of two dipoles are shown in figure. The resultant dipole moment will be directed along \[OP\] where\[P=(a,\,\,a,\,\,0)\]. The magnitude of resultant dipole moment is                 \[p=\sqrt{{{p}^{2}}+{{p}^{2}}}=\sqrt{{{(qa)}^{2}}+{{(qa)}^{2}}}\]                     \[=\sqrt{2}qa\]