Torque on a dipole in a uniform electric field:
As shown in fig, consider an electric dipole consisting of charge +q and -Q and of length 2a placed in a uniform electric field E making an angle θ with it. It has a dipole moment of magnitude.
P=q x 2a
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| Torque on a dipole in a uniform electric field |
Force exerted on charge +q by field E⃗ =+qE (along with E )
Force exerted on the charge -q by field E⃗ =−qE (opposite to E)
Torque = Either force x Perpendicular distance between the two forces
τ=qE×2a.sinθ=(q×2a)E.sinθ
Where (p=q x 2a)
τ=pEsinθ
As the direction of toque τ is perpendicular to both p and E, so we can write
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| Simulation of Torque on a dipole in a uniform electric field |
Hence the net translating force on a dipole in a uniform electric field is zero. But the two equal and opposite forces act at different points of the dipole. They form a couple that exerts a torque.
Torque = Either force x Perpendicular distance between the two forces
τ=qE×2a.sinθ=(q×2a)E.sinθ
Where (p=q x 2a)
τ=pEsinθ
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| The direction of torque as given by right-hand screw rule |
As the direction of toque τ is perpendicular to both p and E, so we can write
τ→=p→×E→
When the dipole is released , the torque tends to align the dipole with the field E i.e. , tends to reduce angle θ to 0.When the dipole gets aligned with E the torque becomes zero.
τ=0 ( torque align with E)
Clearly , the torque on the dipole will be maximum when the dipole is held perpendicular to E. Thus
τmax =p.Esin90=p.E
When the dipole is released , the torque tends to align the dipole with the field E i.e. , tends to reduce angle θ to 0.When the dipole gets aligned with E the torque becomes zero.
τ=0 ( torque align with E)
Clearly , the torque on the dipole will be maximum when the dipole is held perpendicular to E. Thus
τmax =p.Esin90=p.E
Dipole moment:
τ=pEsinθ
If E=1 unit, θ=90 τ = p
Hence dipole moment may be defined as the torque acting on an electric dipole , placed perpendicular to a uniform electric field of unit strength.