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  • An electric dipole has a fixed dipole moment , which makes angle θ with respect to x-axis.  When subjected to an electric field it exp

An electric dipole has fixed dipole moment \vec{P}, which makes angle θ with respect to x-axis. When subjected to an electric field \overrightarrow{\mathbf{E}_{1}}=\mathbf{E} \hat{\mathbf{i}} it experiences a torque \overrightarrow{\mathrm{T}_{1}}=T \mathrm{k}. When subjected to another electric field \overrightarrow{\mathbf{E}_{2}}=\sqrt{\mathbf{3}} \mathbf{E}_{1} \hat{\mathbf{j}} it experiences a torque \overrightarrow{\mathbf{T}_{2}}=-\overrightarrow{\mathbf{T}_{1}} The angle θ is :

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\\\text {From } \vec{T}=\vec{p} \times \vec{E} \\ T \hat{k}=\tau \hat{k}=\left(p_{x} \hat{i}+p_{y} \hat{j}\right) \times (E \hat{i}+\sqrt{3} E \hat{j}) \\ =p_{x} \times \sqrt{3} E \hat{k}+p_{y} E(-\hat{k}) \\ 0=E \hat{k}\left(\sqrt{3} p_{x}-p_{y}\right) \\ \frac{p_{y}}{p_{x}}=\sqrt{3} \\ \therefore \tan \theta=\sqrt{3} \\ \theta=60^{\circ}

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