Module 3 : MAGNETIC FIELD
Lecture 15 : Biot- Savarts' Law
Example 6
 

Field due to a circular coil on its axis
Consider the current loop to be in the x-y plane, which is taken perpendicular to the plane of the paper in which the axis to the loop (z-axis) lies. Since all length elements on the circumference of the ring are perpendicular to $\vec r$, the magnitude of the field at a point P is given by

\begin{displaymath}dB = \frac{\mu_0I}{4\pi}\frac{dl}{r^2}\end{displaymath}

The direction of the field due to every element is in the plane of the paper and perpendicular to $\vec r$, as shown. Corresponding to every element $\vec{dl}$on the circumference of the circle, there is a diametrically opposite element which gives a magnetic field $\vec{dB}$in a direction such that the component of $\vec{dB}$perpendicular to the axis cancel out in pairs.

\includegraphics{fig3.20.eps}

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