An electric dipole has fixed dipole moment p- which makes angle - with respect to x-axis- When subjected to an electric field E1-E- it experiences a torque T1-k- When subjected to another electric field E2-3E1- it experiences a torque T2-T1- The angle - is -

The correct option is A 60^o T=p×E p=pxî+pyĵ Tk̂=(Px î+Py ĵ)× (Eî) ⇒ Py= TE Also, Tk̂=(Px î+ Py ĵ)× (√(3)E ĵ) ⇒ Px= T√(3)E ...

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Byju's Answer

Standard XII

Chemistry

Mathematics of Dipole Moment

An electric d...

Question

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

90^{o}

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30^{o}

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45^{o}

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60^{o}

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Solution

The correct option is A $60^{o}$
$\to T = \to p \times \to E$
$\to p = p x^i + p y^j$
$T^k = (P x^i + P y^j) \times (E^i)$
$\Rightarrow P y = - \frac{T}{E}$
Also,
$- T^k = (P x^i + P y^j) \times (\sqrt{3} E^j)$
$\Rightarrow P x = - \frac{T}{\sqrt{3} E}$
$t a n θ = \frac{P x}{P y} = \sqrt{3}$
$θ = 60^{0}$

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An electric dipole has 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 a torque →T2=−→T1. The angle θ is :

The correct option is A 60o→T=→p×→E→p=px^i+py^jT^k=(Px^i+Py^j)×(E^i)⇒Py=−TEAlso,−T^k=(Px^i+Py^j)×(√3E^j)⇒Px=−T√3Etanθ=PxPy=√3θ=600