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प्रश्न
(i)Obtain the expression for the torque `vecτ` experienced by an electric dipole of dipole moment `vecP` in a uniform electric field, `vecE` .
(ii) What will happen if the field were not uniform?
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उत्तर
(i) Consider an electric dipole consisting of charges −q and +q and of length 2a placed in a uniform electric field making an angle θ with electric field.
Force on charge −q at `A=-qvecE`(opposite to`vecE`)
Force on charge +q at `B=qvecE`(along`vecE`)
Electric dipole is under the action of two equal and unlike parallel forces, which give rise to a torque on the dipole.
τ = Force × Perpendicular distance between the two forces
τ = qE (AN) = qE (2a sin θ)
τ = q(2a) E sinθ
τ = pE sinθ
`therefore vectau=vecPxxvecE`
(ii) If the electric field in not uniform then both the charges of the dipole will experience a different force (not equal and opposite) at slightly different positions in the field and hence a net force acts on the dipole in a nonuniform electric field. Also, a net torque acts on the dipole which depends on the location of the dipole in the nonuniform electric field.
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संबंधित प्रश्न
- Define torque acting on a dipole of dipole moment \[\vec{p}\] placed in a uniform electric field \[\vec{E}\] Express it in the vector from and point out the direction along which it acts. Express it in the vector from and point out the direction along which it acts.
- What happens if the field is non-uniform?
- What would happen if the external field
\[\vec{E}\] is increasing (i) parallel to \[\vec{p}\] and (ii) anti-parallel to \[\vec{p}\]?
Define dipole moment of an electric dipole. Is it a scalar or a vector?
In which orientation, a dipole placed in a uniform electric field is in (i) stable, (ii) unstable equilibrium?
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(a) The flux of the electric field through the sphere is zero.
(b) The electric field is zero at every point of the sphere.
(c) The electric field is not zero anywhere on the sphere.
(d) The electric field is zero on a circle on the sphere.
Two particles A and B, of opposite charges 2.0 × 10−6 C and −2.0 × 10−6 C, are placed at a separation of 1.0 cm. Calculate the electric field at a point on the perpendicular bisector of the dipole and 1.0 m away from the centre.
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