Chapter 5 Solutions — Magnetism and Matter

Exercises

1. 1.
   A short bar magnet placed with its axis at 30° with a uniform external magnetic field of 0.25 T experiences a torque of magnitude equal to 4.5 × 10^-2 J. What is the magnitude of magnetic moment of the magnet?
2. 2.
   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

   • (a) stable, and
   • (b) unstable equilibrium? What is the potential energy of the magnet in each case?
3. 3.
   A closely wound solenoid of 800 turns and area of cross section 2.5 × 10^-4 m^2 carries a current of 3.0 A. Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?
4. 4.
   If the solenoid in Exercise 5.3 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?
5. 5.
   A bar magnet of magnetic moment 1.5 J T^-1 lies aligned with the direction of a uniform magnetic field of 0.22 T.

   • (a) What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment:
   • (i) normal to the field direction,
   • (ii) opposite to the field direction?
   • (b) What is the torque on the magnet in cases
   • (i) and (ii)?
6. 6.
   A closely wound solenoid of 2000 turns and area of cross-section 1.6 × 10^-4 m^2, carrying a current of 4.0 A, is suspended through its centre allowing it to turn in a horizontal plane.

   • (a) What is the magnetic moment associated with the solenoid?
   • (b) What is the force and torque on the solenoid if a uniform horizontal magnetic field of 7.5 × 10^-2 T is set up at an angle of 30° with the axis of…
7. 7.
   A short bar magnet has a magnetic moment of 0.48 J T^-1. Give the direction and magnitude of the magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on

   • (a) the axis,
   • (b) the equatorial lines (normal bisector) of the magnet.