question_answer 54)

  Consider a circular current-carrying loop of radius R in the x-y plane with centre at origin. Consider the line integral (L) =taken along z-axis. (a) Show that  (L) monotonically increases with L. (b) Use an appropriate Amperian loop to show that, where is the current in the wire. (c) Verify directly the above result. (d) Suppose we replace the circular coil by a square coil of sides R carrying the same, current . What can you say about (L) and ?      

Answer:

                  (a) As circular loop carrying current is lying, in x-y plane, the magnetic field  is along the z-axis, in the direction of line integral. Hence, line integral, Therefore  is monotonically increasing with L. (b) Consider a closed amperian path PQRP as shown in Fig. 3(EP).9. According to Ampere circuital law, line integral of  over the closed path PQRP is            or               ?.. When , then the value of (c) Magnetic field at a point on the axis of circular coil at a distance z from the centre of a circular coil of radius R carrying current is Put z = (d) If circular coil is replaced by a square coil of side R, carrying the same current , then Using arguments as in (b)