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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
An electric dipole of dipole moment`vecp` consists of point charges +q and −q separated by a distance 2a apart. Deduce the expression for the electric field `vecE` due to the dipole at a distance x from the centre of the dipole on its axial line in terms of the dipole moment `vecp`. Hence show that in the limit x>> a, `vecE->2vecp"/"(4piepsilon_0x^3)`
Derive the expression for the electric potential due to an electric dipole at a point on its axial line.
- 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 \[\vec{p}\]?
An electric dipole of length 1 cm, which placed with its axis making an angle of 60° with uniform electric field, experience a torque of \[6\sqrt{3} Nm\] . Calculate the potential energy of the dipole if it has charge ±2 nC.
In which orientation, a dipole placed in a uniform electric field is in (i) stable, (ii) unstable equilibrium?
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 axis of the dipole 1.0 cm away from the centre.
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The unit of electric dipole moment is ______.
In a non-uniform electric field, electric dipole experiences:-
In an electric dipole, what is the locus of a point having zero potential?
