A magnetic dipole of moment μ is held in a uniform magnetic field of magnitude B. The dipole axis makes an angle θ with the field direction.
a. (i) Write the mathematical expression for the potential energy of the dipole in the field, clearly defining each symbol used.
b. (ii) Draw a neat, labelled graph showing the variation of the potential energy with θ for 0≤θ≤2π.
c. (iii) From the graph, identify the orientations that correspond to stable and unstable equilibrium. Give a reason for each.
d. (iv) Explain, with reference to the expression obtained in (i), why the dipole tends to rotate towards the position of stable equilibrium when slightly disturbed.