A single circular loop of radius R carries a steady current I. Point P lies on the axis of the loop at a distance x from its centre.
a. (i) State the fundamental law that relates the magnetic field produced by an element of a current-carrying conductor to the position vector of the point of observation.
b. (ii) Starting from the law stated in part (i), obtain an expression for the magnitude of the magnetic field B at point P in terms of μ0,I,R and x. Clearly indicate the direction of B.
c. (iii) Hence obtain the value of B at the centre of the loop and also for points far away on the axis (x≫R). Comment on how B depends on x in the far-field region.
d. (iv) How does the expression in part (ii) get modified if the loop is replaced by a closely wound coil of N turns carrying the same current I? Write the new expression without derivation.