An electric dipole has a fixed dipole moment p- - which makes angle - with respect to x -axis- When subjected to an electric field E 1 - E - - it experiences a torque T- 1 - -k- - When subjected to another electric field E- 2 - - 3 E 1 - it experiences torque T- 2 - - T- 1 - The angle - is -

The correct option is A 60 ^ ∘ Torque amp; τ=p̅×E̅ Given p̅ amp;=p_x1̂+p_y_& τ=γk̂ #10; amp; ∼k̂=(p_kî+p_y) × Eî #10; [ ...

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Standard XII

Chemistry

Properties of Water

An electric d...

Question

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

60^{\circ}

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30^{\circ}

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90^{\circ}

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45^{\circ}

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Solution

The correct option is A $60^{\circ}$
$\begin{matrix} Torque & τ = ¯ p \times ¯ E Given ¯ p & = p_{x}^1 + p_{y} {^ȷ}_{&} τ = γ^k \sim^k = (p_{k}^i + p_{y}^ȷ) \times E^i \end{matrix}$
$\begin{matrix} τ^k = 0 + P_{y} E (-^k) P_{y} = \frac{- γ}{E} Torque =↑^k, ¯ E = \sqrt{3} E^j \end{matrix}$
$\begin{matrix} - γ^k = P_{n} \sqrt{3} E^k P_{x} = \frac{- ↑}{\sqrt{3} E} tan θ = \frac{P_{y}}{P_{n}} = δ_{3} \end{matrix}$
$\begin{matrix} \Rightarrow θ = 60^{\circ} Hence option A is correct \end{matrix}$

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An electric dipole has a fixed dipole moment →p , which makes angle θ with respect to 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 torque →T2=−→T1⋅ The angle θ is :

The correct option is A 60∘ Torque τ=¯p×¯E Given ¯p=px^1+py^ȷ&τ=γ^k∼^k=(pk^i+py^ȷ)×E^iτ^k=0+PyE(−^k)Py=−γE Torque =↑^k,¯E=√3E^j−γ^k=Pn√3E^kPx=−↑√3Etanθ=PyPn=δ3⇒θ=60∘ Hence option A is correct