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Three point charges +q, −q and +q are placed at points (x = 0, y = a, z = 0), (x = 0, y = −a, 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 joining 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 answer: √2qa along the line joining points (x = 0, y = 0, z = 0) and (x = a, y = a, z = 0)

Solution

The electric dipole moment is given by the vector sum of the dipole moments of the individual charge pairs. The dipole moment due to the charges at (0, a, 0) and (0, -a, 0) is along the y-axis, and the dipole moment due to the charges at (a, 0, 0) and the center of the other two charges is along the x-axis. The resultant dipole moment has a magnitude of √2qa and is directed along the line joining (0, 0, 0) and (a, a, 0).

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