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Question
A dipole with dipole moment 3.60 nC−m is oriented at 60∘ to an electric field of magnitude 4×109 N/C, how much work is required to rotate the dipole until it is antiparallel to field.
A dipole with dipole moment 3.60 nC−m is oriented at 60∘ to an electric field of magnitude 4×109 N/C, how much work is required to rotate the dipole until it is antiparallel to field.
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Solution
The correct option is A 21.6 J
Potential energy of a dipole at an angle θ with electric field
U=−→p.→E=−pE cos θ
To rotate the dipole (slowly), we need to work on dipole so that the potential energy is increased. W=ΔU=Uf−Ui
Ui=−pE cos 60=−pE2
Uf=−pE cos 180=+pE
W=pE−(−pE2)=3pE2
=32×3.6×10−9×4×109
=3×3.6×2=7.2×3=21.6 J
Potential energy of a dipole at an angle θ with electric field
U=−→p.→E=−pE cos θ
To rotate the dipole (slowly), we need to work on dipole so that the potential energy is increased. W=ΔU=Uf−Ui
Ui=−pE cos 60=−pE2
Uf=−pE cos 180=+pE
W=pE−(−pE2)=3pE2
=32×3.6×10−9×4×109
=3×3.6×2=7.2×3=21.6 J
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