Q.A solenoid of length $\pi$ m and 5 cm in diameter has a winding of 1000 turns and carries a current of 5 A. Calculate the magnetic field at its centre along the axis.

A solenoid is a long, tightly and closely wound helical coil of wire. In the idealised limit of an infinitely long solenoid, the magnetic field inside is perfectly uniform and directed along the solenoid's axis, while the field outside is exactly zero everywhere. Applying Ampere's law to a rectangular Amperian loop with one side inside the solenoid (parallel to the axis) and the opposite side outside makes three of the four sides' contributions to the line integral vanish, leaving $BL=\mu_0(nLi)$, where n is the number of turns per unit length and i the current -- giving the field inside as $B=\mu_0ni$, notably independent of the solenoid's radius. …