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 :

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