(a) Let I be the current carried by a wire bent into a planar loop. Place the origin of coordinates at an observation point P in the plane of the loop. Show that the magnitude of the magnetic field at the point P is

where r(φ) is the distance from the origin of coordinates at P to the point on the loop located at an angle φ from the positive x-axis.
(b) Show that the magnetic field at the center of a current-carrying wire bent into an ellipse with major and minor axes 2a and 2b is proportional to a complete elliptic integral of the second kind. Show that you get easily understandable answers when a = b and when a →∞ with b fixed.
(c) An infinitesimally thin wire is wound in the form of a planar coil which can be modeled using an effective surface current density Find the magnetic field at a point P on the symmetry axis of the coil. Express your answer in terms of the angle α subtended by the coil at P.

B(P) = 0 r()