Answer Happy

(a) i) Write the expression for the magnetic field B(r) due to surface and volume current distributions. ii) Write the Ampere's law due to current I in its integral form. iii) By applying the Stoke's theorem, derive the expression for the Ampere's law in the differential form. (b) i) Why is it possible to define magnetic field B in term of a vector potential À? Write the expression for the vector potential À(7) due to surface and volume 11) current distributions. iii) Define the magnetic dipole m and magnetization M. (c) A long circular cylinder of radius R (Figure 1) carries a magnetization M = ks² where k is a constant, s is the distance from the axis, and is the usual azimuthal unit vector. i) Determine the magnetic field B(r) due to M, for points inside and outside the cylinder. ii) Sketch the field lines of the magnetic field B in any plane containing the z-axis. Figure 1 R