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Derive the expression for the torque acting on an electric dipole, when it is held in a uniform electric field. Identify the orientation of the dipole in the electric field, in which it attains stable equilibrium. |
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Answer» SOLUTION :Consider an electric dipole AB placed in a uniform electric field `vecE` oriented at an angle `theta` with the field. As shown, forces qE and qE act on the two charges in mutually opposite directions. As the two forces act at two different points non-linearly, they constitute a couple whose torque is given by:  torque `tau =(qE).` Normal DISTANCE between the forces =`qE 2a sin theta= PE sin theta "" [ :.p =q(2a)]` The torque has a tendency to align the dipole along the direction of electric field. In vector notation, we can write that, `vectau= vecpxxvecE.` When electric dipole is parallel to the electric field `vecE, theta=0^(@)` and so the torque `vectau=vec0` . Moreover, potential energy of dipole [U= -pE sin `theta`] is minimum having a value U = -pE. So this REPRESENTS the stable equilibrium POSITION of dipole. |
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