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Derive an expression for torque oversett...

Derive an expression for torque `oversetto tau ` experienced by an electric dipole of dipole moment `oversetto p` kept in uniform electric ` oversetto E.` What will happen if the field were not uniform?

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Consider an electric dipole AB placed in a uniform electric field `oversetto E ` oriented at an angle ` theta ` with the field.
As shown in forces qE and qE act on the two charges in mutually opposite directions. Consquently, net translational force on dipole is zero and there is no translatory motion of dipole. However, as the two forces act at two different points non-linearly. they constitute a couple whose torque is given by:
torque ` " " torque =(qE) . `Normal distance between the forces
`" "=qE 2 a sin theta =qE sin theta `
The torque has tendency to align the dipole along the direction of electric field. In vector notation, we can write that ,
` " " oversetto tau =oversetto p xx oversetto E `
If the electric field were not uniform then the dipole will experience a net translatory forces as well as a torque.
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Knowledge Check

  • An electric dipole of dipole moment p is placed in a uniform external electric field E. Then, the

    A
    toeque experienced by the dipole is `E xxp`
    B
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  • The torque tau acting on an electric dipole of dipole momtn vec(p) in an electric field vec( E ) is

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    `vec(tau) = p. vec(E )`
    D
    `vec(tau) = vec(p) E`

  • A dipole of dipole moment vec(P) is placed in uniform electric field vec(E) , then torque acting on it is given by

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    `vec(tau)=vec(P).vec(E)`
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    `vec(tau)=vec(P)xx vec(E)`
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