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Question:

An electric dipole has fixed dipole moment →p, which makes angle θ with respect to the x-axis. When subjected to an electric field →E₁=E^i, it experiences a torque →T₁=τ^k. When subjected to another electric field →E₂=√3E₁^j it experiences a torque →T₂=−→T₁. The angle θ is:

90o

60o

30o

45o

Solution:

→T=→p×→E
→p=px^i+py^j
T^k=(px^i+py^j)×(E^i)⇒py=−τ/E
Also, −T^k=(px^i+py^j)×(√3E^j)⇒px=−τ/(√3E)
tanθ=px/py=√3
θ=60o