An electric dipole has fixed dipole moment p → , which makes angle θ with respect to x - axis.…

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=Ei^, it experiences a torque T→1=τk^. When subjected to another electric field E→2= 3 E1j^ it experiences a torque T→2=-T→1 . The angle θ is:
  1. 90o
  2. 30o
  3. 45o
  4. 60o

Solution

P→=Pcos⁡θi^+Psin⁡θj^

T→=Pcos⁡θi^+Psin⁡θj^×Ei^

=-PEsin⁡θk^

T→2=Pcos⁡θi^+Psin⁡θj^×3Ej^

= 3PEcos⁡θk^

T→2= -T→1

∴    sin⁡θ= 3cos⁡θ

∴    tan⁡θ= 3

∴   θ=60o

Asked in: JEE Main 2017 (02 Apr)

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