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°, the torque and the potential energy of the dipole will respectively be

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°, the torque and the potential energy of the dipole will respectively be (A)  pE sin θ , -pE cos θ  (B)  pE sin θ , -2pE cos θ  (C)  pE sin θ , 2pE cos θ  (D)  pE cos θ , -pE sin θ

Tardigrade Admin · Accepted Answer

Potential energy of the dipole U =-∫ T dB =-∫ limitsπ / 2θ PE sin θ d θ = PE ( cos θ-0)=- PE cos θ and potential energy = PE sin θ.

$pE sin θ, - pE cos θ$

$pE sin θ, - 2 pE cos θ$

$pE sin θ, 2 pE cos θ$

$pE cos θ, - pE sin θ$

Potential energy of the dipole
$U = - \int T d B = - π /2 \int θ PE sin θ d θ$
$= PE (cos θ - 0) = - PE cos θ$
and potential energy $= PE sin θ$ .

pEsinθ,−pEcosθ

pEsinθ,−2pEcosθ

pEsinθ,2pEcosθ

pEcosθ,−pEsinθ

Potential energy of the dipole U=−∫TdB=−π/2∫θ​PEsinθdθ =PE(cosθ−0)=−PEcosθ and potential energy =PEsinθ.

$pE sin θ, - pE cos θ$

$pE sin θ, - 2 pE cos θ$

$pE sin θ, 2 pE cos θ$

$pE cos θ, - pE sin θ$

Potential energy of the dipole
$U = - \int T d B = - π /2 \int θ PE sin θ d θ$
$= PE (cos θ - 0) = - PE cos θ$
and potential energy $= PE sin θ$ .