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

T=p×E p=p_xî+p_yĵ Tk̂=(p_x î+p_y ĵ)× (Eî) ⇒ p_y= TE Also, Tk̂=(p_x î+ p_y ĵ)× (√(3)E ĵ) nbsp; ⇒ p_x= T√(3)E tan θ=p_yp_x= √(3) ⇒θ =60^0 ...

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Standard XII

Mathematics

Determinant

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

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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 D 60o→T=→p×→E →p=px^i+py^j T^k=(px^i+py^j)×(E^i) ⇒py=−TE Also, −T^k=(px^i+py^j)×(√3E^j) ⇒px=−T√3E tan θ=pypx=√3 ⇒θ=600