Advertisements
Advertisements
Question
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 a stable equilibrium.
Advertisements
Solution
Force acting on −q is −qE.
Force acting on +q is qE.
These two forces are equal and opposite to each other. Hence, a torque on the dipole is developed.
Torque = Force × perpendicular distance between the forces
Or, τ = qE × 2 a sin θ
Or, τ = (q × 2a) E sin θ
∴ τ = PE sin θ
Where P is the dipole moment.
Dipole will attain stable equilibrium when it is oriented along the direction of electric field.
RELATED QUESTIONS
Deduce the expression for the torque acting on a dipole of dipole moment `vecp` in the presence of a uniform electric field `vecE`
In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of 105 NC−1 per metre. What are the force and torque experienced by a system having a total dipole moment equal to 10−7 Cm in the negative z-direction?
An electric dipole is placed in a uniform electric field. The net electric force on the dipole
A long bar magnet has a pole strength of 10 Am. Find the magnetic field at a point on the axis of the magnet at a distance of 5 cm from the north pole of the magnet.
Maximum torque acting on an electric dipole of moment 3×10-29 Cm in a uniform electric field E is 6 × 10-25 Nm. Find E.
An electric dipole of dipole moment `vecP` is placed in a uniform electric field `vecE` with its axis inclined to the field. Write an expression for the torque `vecT` experienced by the dipole in vector form. Show diagrammatically how the dipole should be kept in the electric field so that the torque acting on it is:
- maximum
- Zero
Deduce the expression for the torque `vec"τ"` acting on a planar loop of area `vec"A"` acting on a planar loop of area `vec"B"`. If the loop is free to rotate, what would be its orientation in stable equilibrium?
A short bar magnet of magnetic moment m = 0.32 J T–1 is placed in a uniform magnetic field of 0.15 T. If the bar is free to rotate in the plane of the field, which orientation would correspond to its
- stable, and
- unstable equilibrium?
What is the potential energy of the magnet in each case?
If the solenoid is free to turn about the vertical direction and a uniform horizontal magnetic field of 0.25 T is applied, what is the magnitude of torque on the solenoid when its axis makes an angle of 30° with the direction of applied field?
Assertion: The poles of magnet can not be separated by breaking into two pieces.
Reason: The magnetic moment will be reduced to half when a magnet is broken into two equal pieces.
Let the magnetic field on earth be modelled by that of a point magnetic dipole at the centre of earth. The angle of dip at a point on the geographical equator is ______.
An electric dipole of dipole moment 2 × 10-8 C-m in a uniform electric field experiences a maximum torque of 6 × 10-4 N-m. The magnitude of the electric field is ______.
An electric dipole of length 2 cm is placed at an angle of 30° with an electric field 2 × 105 N/C. If the dipole experiences a torque of 8 × 10-3 Nm, the magnitude of either charge of the dipole is ______.
