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

The resultant field is parallel to the axis, its direction being along the positive z-axis for the current direction shown in the figure. The net field is

\begin{eqnarray*} \vec B &=& \frac{\mu_0 I}{4\pi}\int\frac{dl}{r^2}\cos\theta\\ ... ...0 I\cos\theta}{4\pi r^2}2\pi a = \frac{\mu_0 Ia\cos\theta}{2r^2} \end{eqnarray*}

In terms of the distance $z$of the point P and the radius $a$, we have

\begin{displaymath}B = \frac{\mu_0 I}{2}\frac{a^2}{(a^2+z^2)^{3/2}}\end{displaymath}

The direction of the magnetic field is determined by the following Right Hand Rule.

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