Three point charges +q, –q and +q are placed at points

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Three point charges +q, –q 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

1. √2qa along the line joini points (x = 0, y = 0, z = 0) and (x = a, y = a, z = 0)
2. qa along the line joining points (x = 0, y = 0, z = 0) and (x = a, y = a, z = 0)
3. √2qa along +ve x direction
4. √2qa along +ve y direction

Correct Option: A

Three point charges +q, –2q and +q are placed at points B (x = 0, y = a, z = 0), O (x = 0, y = 0, z = 0) and A(x = a, y = 0, z = 0) The system consists of two dipole moment vectors due to (+q and –q) and again due to (+q and –q) charges having equal magnitudes qa units – one along OA^{^→} and other along OB^{^→} . Hence, net dipole moment,
p_net = √(qa)² + (qa)² = √2 qa along OP^{^→} at an angle 45° with positive X-axis.