An electric dipole of moment p is placed in an electric field of intensity E- The dipole acquires a position such that the axis of the dipole makes an angle - with the direction of the field- Assuming that the potential energy of the dipole to be zero when - - 90- the torque and the potential energy of the dipole will respectively be

Torque acting on the dipole is given by, τ=p×E ⇒τ= pEsinθ Potential of the dipole, U= q(Δ V) ⇒ U= q(E .d) ⇒ U= q(d .E) ⇒ U= (p .E) ⇒ U=( pEcosθ) Hence, ...

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Question

An electric dipole of moment $p$ is placed in an electric field of intensity $E$ . The dipole acquires a position such that the axis of the dipole makes an angle $θ$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $θ = 90^{\circ}$ , the torque and the potential energy of the dipole will respectively be

p E sin θ, - p E cos θ

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p E sin θ, - 2 p E cos θ

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p E sin θ, 2 p E cos θ

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p E cos θ, - p E sin θ

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Solution

The correct option is A $p E sin θ, - p E cos θ$
Torque acting on the dipole is given by,
$\to τ = \to p \times \to E$

$\Rightarrow τ = p E sin θ$

Potential of the dipole,

$U = - q (Δ V)$

$\Rightarrow U = - q (\to E . \to d)$

$\Rightarrow U = - q (\to d . \to E)$

$\Rightarrow U = - (\to p . \to E)$

$\Rightarrow U = (- p E cos θ)$

Hence, option $(C)$ is correct.

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The correct option is A pEsinθ,−pEcosθTorque acting on the dipole is given by, →τ=→p×→E ⇒τ=pEsinθ Potential of the dipole, U=−q(ΔV) ⇒U=−q(→E.→d) ⇒U=−q(→d.→E) ⇒U=−(→p.→E) ⇒U=(−pEcosθ) Hence, option (C) is correct.