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An electric dipole has a fixed dipole moment p that makes an angle theta with the x-axis. In a field E1 = E i (along x), it feels a torque tau1 = tau k. In a different field E2 = sqrt(3) E j (along y), the torque becomes tau2 = -tau1. Find theta.
- 60 deg
- 90 deg
- 30 deg
- 45 deg
Correct answer: 60 deg
Solution
The angle between p and E1 (x-axis) is theta, giving torque magnitude pE sin(theta). The angle between p and E2 (y-axis) is (90 - theta), giving p*sqrt(3)E sin(90 - theta) = sqrt(3)pE cos(theta). Equating magnitudes (the signs are opposite as required) gives tan(theta) = sqrt(3), so theta = 60 deg.
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