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Three point charges 2q, -q and -q are located at the positions (0, a, a), (0, a, -a) and (0, 0, -a) respectively. Find the dipole moment of this charge distribution.

1. 2qa in the y-z plane at tan⁻¹(1/4) with the z-axis
2. sqrt(17) qa in the y-z plane at tan⁻¹(1/4) with the z-axis
3. sqrt(5) qa in the x-y plane at tan⁻¹(4) with the y-axis
4. 4qa in the x-y plane at tan⁻¹(4) with the y-axis

Correct answer: sqrt(17) qa in the y-z plane at tan⁻¹(1/4) with the z-axis

Solution

p = 2q(0,a,a) + (-q)(0,a,-a) + (-q)(0,0,-a) = (0, 2qa - qa - 0, 2qa + qa + qa) = (0, qa, 4qa). Its magnitude is qa*sqrt(1² + 4²) = sqrt(17) qa, lying in the y-z plane. The angle with the z-axis satisfies tan(angle) = p_y / p_z = qa / 4qa = 1/4, i.e. tan⁻¹(1/4) from the z-axis.

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