Magnetism and Matter

Magnetism and Matter studies magnets and the magnetic behaviour of materials, connecting the bar magnet familiar from school with the current loops of the previous chapter. In this chapter you will learn about magnetic field lines and their properties, and see that a bar magnet behaves like a current-carrying solenoid, so both are magnetic dipoles with a magnetic moment m. You will derive the magnetic field of a bar magnet at points on its axis and on its equatorial line, and find the torque and potential energy of a magnetic dipole in a uniform magnetic field. Gauss's law for magnetism shows that isolated magnetic poles do not exist. The second half of the chapter deals with magnetic properties of materials. You will define magnetisation, magnetic intensity, susceptibility and relative permeability, and learn the relation B = mu0(H + M). You will classify materials as diamagnetic, paramagnetic or ferromagnetic, explain their behaviour in terms of atomic magnetic moments and domains, and study the effect of temperature through Curie's law and the Curie temperature.

Detailed Worksheet: Magnetism and Matter Section A - Definitions (10 marks) 1. State four properties of magnetic field lines. (2 marks) 2. Define magnetic dipole moment of a bar magnet and of a current loop. Write its SI unit. (2 marks) 3. State Gauss's law for magnetism. What does it imply? (2 marks) 4. Define magnetisation and magnetic susceptibility. (2 marks) 5. State Curie's law for paramagnetic materials. What is the Curie temperature? (2 marks) Section B - Calculations and Applications (15 marks) 6. A short bar magnet placed with its axis at 30 degrees to a uniform magnetic field of 0.08 T experiences a torque of 0.016 N m. Find its magnetic moment. Find its potential energy when aligned with the field. (3 marks) 7. A short bar magnet has a magnetic moment of 0.48 J/T. Find the magnetic field at a distance of 10 cm from its centre on (i) its axis and (ii) its equatorial line (mu0/(4 pi) = 10^-7 T m/A). (3 marks) 8. Find the work done in rotating the magnet of question 6 from the position aligned with the field to the position opposite to the field. (3 marks) 9. A closely wound solenoid of 800 turns and area of cross-section 2.5 x 10^-4 m^2 carries a current of 3.0 A. Find its magnetic moment. In which direction does it act? (3 marks) 10. A solenoid has 1,000 turns per metre and carries a current of 2 A. Its core has relative permeability 400. Find the magnetic intensity H, the magnetic field B, the magnetisation M and the susceptibility of the core. (3 marks) Section C - Diagrams (10 marks) 11. Draw the magnetic field lines of a bar magnet and of a current-carrying solenoid, and show their similarity. (4 marks) 12. Draw diagrams showing how field lines behave when (i) a diamagnetic and (ii) a paramagnetic substance is placed in a uniform magnetic field. (3 marks) 13. Draw a diagram showing a magnetic dipole in a uniform magnetic field, the angle theta, and the torque acting on it. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. The susceptibility of a paramagnetic salt is 2.4 x 10^-4 at 300 K. Using Curie's law, find its susceptibility at 200 K. Explain why susceptibility increases on cooling and why ferromagnets become paramagnetic above the Curie temperature. (5 marks) 15. Compare diamagnetic, paramagnetic and ferromagnetic materials on the basis of (i) susceptibility, (ii) relative permeability, (iii) behaviour in a non-uniform field, (iv) effect of temperature and (v) examples. (5 marks) 16. Compare magnetic field lines with electric field lines. Explain why magnetic field lines form closed loops and why the net magnetic flux through any closed surface is zero. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Use mu0 = 4 pi x 10^-7 T m/A and show units. Draw neat diagrams.