An electric dipole has fixed dipole moment p → , which makes angle θ with respect to x - axis. When subjected to an electric field E → 1 = E i ^ , it experiences a torque T → 1 = τ k ^ . When subjecte

Question

An electric dipole has fixed dipole moment p → , which makes angle θ with respect to x - axis. When subjected to an electric field E → 1 = E i ^ , it experiences a torque T → 1 = τ k ^ . When subjected to another electric field E → 2 = 3 E 1 j ^ it experiences a torque T → 2 = - T → 1 . The angle θ is:

TestHub · Accepted Answer

P → = P cos ⁡ θ i ^ + P sin ⁡ θ j ^ T → = P cos ⁡ θ i ^ + P sin ⁡ θ j ^ × E i ^ = - P E sin ⁡ θ k ^ T → 2 = P cos ⁡ θ i ^ + P sin ⁡ θ j ^ × 3 E j ^ = 3 P E cos ⁡ θ k ^ T → 2 = - T → 1 ∴ sin ⁡ θ = 3 cos ⁡ θ ∴ tan ⁡ θ = 3 ∴ θ = 60 o

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