. A circular coil of radius a with N turns lies in the xy plane with the z axis through itscentre, as shown in Fig. 1. The magnetic field along

the axis is given by: B(z)=\frac{\mu_{0} N I a^{2}}{2\left(a^{2}+z^{2}\right)^{3 / 2}} :0.20 A, andN =5.0 x 10-Am2 lies along the z axis at a distance of zwhere I is the current. The coil has a =1.0 cm, I =1000. A magneticdipole with magnitude m =+5.0 cm from the centre of the coil. The dipole points along the +z axis. (a) What is the torque on the dipole? (b) What is the magnetic energy of the dipole? (c) What is the force on the dipole? (Hint: make the approximation z? > a².) Byconsidering the coil as a dipole, and making the analogy with bar-magnet dipoles,explain the sign of the force on the dipole. (d) Sketch the dipole's magnetic energy as a function of z, and describe its motion, as-suming that it is free to move without any frictional forces. (Hint: make an analogywith a ball rolling on a curved surface, and apply conservation of energy.) (e) The dipole has a mass of 7.9 x 10-6 kg. What is its maximum speed? (f) The dipole is made of ferromagnetic iron, which has a relative atomic mass of 55.8.Calculate the average dipole moment per iron atom along the z axis in units of theBohr magneton, UB. Explain how this value can be significantly less than uB, eventhough each individual iron atom has a dipole moment of - pg.