Explain with the help of a labelled diagram the distribution of a magnetic field due to a current through a circular loop. Why is it that if a current carrying loop has n turns the field produced at any point is n times as large as that produced by a single turn?

The magnetic field pattern due to a circular coil is as shown in the given figure. At every point of current carrying circular loop, the concentric circles representing the magnetic field around it becomes larger and larger as we move away from the wire. At the center of the loop, the field appears as a straight line.

The magnetic field produced by current-carrying circular wire at a given point depends on:

(1) Amount of current flowing through the wire, $I$

$B\propto I..........\left(1\right)$

(2) The number of turns, $N$

$B\propto N..........\left(2\right)$

There is a circular coil having $N$ turns, the field produced is n times as a large as that produced by a single turn. It happens because the current in each circular turns has the same direction and the field due to each turn just adds up.