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)  \[I=2\] along +y direction

B)  \[I\] along the line joining points (x = 0, y = 0, z = 0) and (x = a, y = a, z = 0)

C)  \[I\] along the line joining points (x = 0, y = 0, z = 0) and (x = a, y = a, z = 0)

D)  \[I\] 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 = (a, a, 0). The magnitude of resultant dipole moment is \[\Rightarrow \] \[{{T}_{f}}=\frac{12}{8}{{T}_{0}}=\frac{3}{2}{{T}_{0}}\] \[p=\sqrt{{{p}^{2}}+{{p}^{2}}}\]