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JEE Main 2017 · 2 Apr · Shift 1, Physics question 14

An electric dipole has a fixed dipole moment p⃗\vec p, which makes angle θ with respect to xx-axis. When subjected to an electric field E⃗1=Ei^\vec E_1=E\hat i, it experiences a torque T⃗1=τk^\vec T_1=\tau\hat k. When subjected to another electric field E⃗2=3E1j^\vec E_2=\sqrt3E_1\hat j it experiences a torque T⃗2=−T⃗1\vec T_2=-\vec T_1. The angle θ is :

Choose one option
Answer and worked solution

Official answer: C

With p⃗=p(cos⁡θ,sin⁡θ,0)\vec p=p(\cos\theta,\sin\theta,0):

  • p⃗×Ei^=−pEsin⁡θ k^\vec p\times E\hat i=-pE\sin\theta\,\hat k;
  • p⃗×3Ej^=3pEcos⁡θ k^\vec p\times\sqrt3E\hat j=\sqrt3pE\cos\theta\,\hat k.

T⃗2=−T⃗1\vec T_2=-\vec T_1 gives 3cos⁡θ=sin⁡θ\sqrt3\cos\theta=\sin\theta, so θ=60∘\theta=60^\circ.

Topics:Electric dipole
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