Advertisements
Advertisements
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?
Advertisements
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.
APPEARS IN
संबंधित प्रश्न
A system has two charges qA = 2.5 × 10−7 C and qB = −2.5 × 10−7 C located at points A: (0, 0, − 15 cm) and B: (0, 0, + 15 cm), respectively. What are the total charge and electric dipole moment of the system?
- 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 electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole.
Two particles, carrying charges −q and +q and and of mass m each, are fixed at the ends of a light rod of length a to form a dipole. The rod is clamped at an end and is placed in a uniform electric field E with the axis of the dipole along the electric field. The rod is slightly tilted and then released. Neglecting gravity, find the time period of small oscillations.
A uniform electric field is prevailing in X - direction in certain region. The coordinates of points P, Q, and R are (0, 0), (2, 0) and (0, 2) respectively. Which of the following alternatives is true for the potentials at these points?
When an electric dipole p is placed in a uniform electric field E then at what angle the value of torque will be maximum?
On the axis and on the equator of an electric dipole for all points ____________.
The ratio of the weight of a man in a stationary lift and in a lift accelerating downwards with a uniform acceleration α is 3 : 2. The acceleration of the lift is:
Polar molecules are the molecules ______.
The electric potential V as a function of distance X is shown in the figure.
The graph of the magnitude of electric field intensity E as a function of X is ______.
