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CBSE Class 12-science Answered

Derive an expression for the torque acting on an electric dipole kept in a uniform electric field. When is this torque maximum? What will happen if the field were not uniform?
Asked by bolojubakesri47 | 15 Jul, 2022, 06:15: PM
Expert Answer
Let a dipole of dipole moment p = ( q d ) is placed in uniform electric field E .
where q is magntiude of each charge and d is distance between charges
Let the dipole makes angle θ with direction of electric field as shown in figure.
As shown in figure each charge is subjected to a force qE , hence a couple of forces acting on dipole .
Moment of couple with respect to centre O. = 2 × ( qE ) × (d/2) sinθ = ( q d ) × E × sinθ
Hence Torque τ acting on electric dipole = ( q d ) × E × sinθ = p × E × sinθ
Torque is maximum when θ = π/2
In uniform electric field , net force acting on dipole is zero . hence there is no linear translational motion
In non uniform electric field , net force will be greater than zero.
Hence dipole gets translational motion in the direction of increasing field .
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