A loop of wire of radius R is in the x-y plane, centered at origin, carries a current I counter-clockwise as viewed from the point on the positive z-axis. We are fascinated in the magnetic field at a point on the z-axis, example: P = (0, 0, z).
(i) Determine the contribution to the magnetic field (in vector form) due to a part of current of length dl at (R, 0, 0)
(ii) Determine the contribution to the magnetic field (in vector form) due to a part of current of length dl at (0, R, 0)
(iii) Find out the contribution to the magnetic field (in vector form) due to a part of current of length dl at (-R, 0, 0)
(iv) Determine the contribution to the magnetic field (in vector form) due to the full loop?