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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 q units - one along OA and other along OB.

1. The electric field at the centre due to the charge on the part ACDB is along OK.
2. By symmetry of the figure, the electric fields at O due to the portions AC and BD are equal in magnitude and opposite in direction. So, they cancel each other.
3. Similarly, the field at O due to CD and AKB are equal in magnitude but opposite in direction.
4. Hence, net dipole moment.

Correct answer: By symmetry of the figure, the electric fields at O due to the portions AC and BD are equal in magnitude and opposite in direction. So, they cancel each other.

Solution

The electric fields at O due to portions AC and BD are equal in magnitude but opposite in direction due to symmetry, leading to their cancellation.

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