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 0 with the direction of the field. Assuming that the potential energy of the dipole to be zero when $θ = 90^{0}$ , the torque and the potential energy of the dipole will respectively be:

p E s i n θ, 2 p E c o s θ

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p E c o s θ, - p E s i n θ

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p E s i n θ, - p E c o s θ

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p E s i n θ, - 2 p E c o s θ

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Solution

The correct option is C $p E s i n θ, - p E c o s θ$

Potential energy of the dipole
$U = - \int T d B$
$= - \int_{π / 2}^{θ} P E sin θ d θ$
$= P E (cos θ - 0) = - P E cos θ$
and potential energy $= P E sin θ$ .

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The correct option is C pEsinθ,−pEcosθPotential energy of the dipoleU=−∫TdB =−∫θπ/2PEsinθdθ =PE(cosθ−0)=−PEcosθand potential energy =PEsinθ.

The correct option is C $p E s i n θ, - p E c o s θ$

Potential energy of the dipole
$U = - \int T d B$
$= - \int_{π / 2}^{θ} P E sin θ d θ$
$= P E (cos θ - 0) = - P E cos θ$
and potential energy $= P E sin θ$ .