An electric dipole has a fixed dipole moment , which makes angle θ with respect to x‑axis. When subjected to an electric field , it experiences a torque . When subjected to another electric field it experiences a torque The angle θ is

Engineering

Physics

Electric Dipole

Question

An electric dipole has a fixed dipole moment $\vec{p}$ , which makes angle θ with respect to x‑axis. When subjected to an electric field $\vec{E_{1}} = E \hat{i}$ , it experiences a torque $\vec{T_{1}} = τ \hat{k}$ . When subjected to another electric field $\vec{E_{2}} = \sqrt{3} E_{1} \hat{j}$ it experiences a torque $\vec{T_{2}} = - \vec{T_{1}}$ The angle θ is

60°

30°

45°

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$\vec{p}$

$\vec{E_{1}} = E \hat{i}$ $\vec{E_{2}} = \sqrt{3} E_{1} \hat{j}$

$\vec{T_{1}} = τ \hat{k}$ $T_{2} = - {\vec{T}}_{1}$

${\vec{T}}_{1} = \vec{P} \times {\vec{E}}_{1}$ $T_{2} = \vec{P} \times {\vec{E}}_{2}$

$(P cosθ \hat{i} + P sinθ \hat{j}) \times E \hat{i}$

= PE sin θ – $\hat{k}$

T₂ = P E $\sqrt{3}$ cos θ $\hat{k}$

Given PE $\sqrt{3}$ cos θ = PE sin θ

$\tan θ = \sqrt{3}$ θ – 60º