question_answer

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

Correct Answer: B

Solution :

 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 z 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 the figure. The resultant dipole moment will be directed along OP where P = (a, a, 0). The magnitude of resultant dipole moment is \[P'=\sqrt{{{P}^{2}}+{{P}^{2}}}=\sqrt{{{(qa)}^{2}}+{{(qa)}^{2}}}=\sqrt{2}qa\]