Consider a planar current loop of N turns, area A, carrying current I, placed in a uniform magnetic field B. The loop can rotate about an axis through its centre and within its own plane.
a. (i) Starting from the expression for the torque acting on the loop, derive an expression for the potential energy of the magnetic dipole as a function of the angle θ between its magnetic moment and the field direction.
b. (ii) Using the result of part (i), obtain a general formula for the work done in rotating the dipole from an initial angle θ1 to a final angle θ2.
c. (iii) For N=50, A=8.0×10−4m2, I=0.30A and B=0.15T, calculate the work required to rotate the loop from θ1=90∘ to θ2=30∘.