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

The Correct Option is B

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,\text{ }y $ and $ z $ and plot the charges with the given coordinates as shown. O is the origin at which $ -2\text{ }q $ 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 $