Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
Given: Moment of the bar magnet, M = 0.32 J T−1
External magnetic field, B = 0.15 T
(a) The bar magnet is aligned along the magnetic field. This system is considered as being in stable equilibrium. Hence, the angle θ, between the bar magnet and the magnetic field is 0°.
The potential energy of the system:
U = `vecM * vecB`
= −MB cos θ
= −0.32 × 0.15 × cos 0°
= −0.32 × 0.15 × 1
= − 0.048 J
(b) The bar magnet is oriented 180° to the magnetic field. Hence, it is in unstable equilibrium.
θ = 180°
Potential energy of the system:
U = `vecM * vecB`
= −MB cos θ
= −MB cos 180°
= −0.32 × 0.15 × (−1)
= +0.048 J
संबंधित प्रश्न
Deduce the expression for the torque acting on a dipole of dipole moment `vecp` in the presence of a uniform electric field `vecE`
An electric dipole with dipole moment 4 × 10−9 C m is aligned at 30° with the direction of a uniform electric field of magnitude 5 × 104 N C−1. Calculate the magnitude of the torque acting on the dipole.
An electric dipole is placed in a uniform electric field. The net electric force on the dipole
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?
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.
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?
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 ______.
When an electric dipole is placed in a uniform electric field, what is the net force acting on the dipole?
For a dipole with moment \[\vec{p}\] placed at angle θ to a uniform electric field \[\vec{E}\], what is the perpendicular distance from the center of the dipole to the line of action of force on either charge?
Using the right-hand screw rule, determine the direction of torque when a dipole moment \[\vec{p}\] is rotated toward an electric field \[\vec{E}\].
At what angle θ between the dipole moment and the electric field is the torque on the dipole maximum?
What is the potential energy of a dipole in unstable equilibrium in a uniform electric field?
What distinguishes the behavior of a dipole in a non-uniform electric field from its behavior in a uniform field?
A dipole with moment p experiences a maximum torque of 4 × 10⁻²¹ N·m in a uniform electric field. What is the strength of the electric field?
When a dipole rotates from θ = 0° to θ = 90° in a uniform electric field, how does its potential energy change?
