Question

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

Answer 1

Suppose a straight conducting wire is bent in the form of a circular loop and a current is passed through it.

We know that the magnetic field produced by a current-carrying straight wire depends inversely on the distance from it.

Similarly, at every point of a current-carrying circular loop, the concentric circles representing the magnetic field around it would become larger and larger as we move away from the wire as shown in the figure.

By the time we reach the center of the circular loop, the arcs of these big circles would appear as straight lines.

Every point on the wire carrying current would give rise to the magnetic field appearing as straight lines at the center of the loop.

By applying the right-hand thumb rule, it is easy to check that every section of the wire contributes to the magnetic field lines in the same direction within the loop.

Now, the magnetic field produced by a current-carrying wire at a given point depends directly on the current passing through it. Therefore, if there is a circular coil having n turns, the field produced is n times as large as that produced by a single turn. This is because the current in each circular turn has the same direction, and the field due to each turn then just adds up.