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

The limits of integration on $\theta$are $\alpha$and $\beta$as shown in the figure. With the above substitution

\begin{displaymath}\vec B = -\frac{\mu_0nI}{2}\int_\alpha^\beta \sin\theta d\theta = \frac{\mu_0 nI}{2}(\cos\alpha-\cos\beta) \hat k\end{displaymath}

For a long solenoid, the field on the axis at points far removed from the ends of the solenoid may be obtained by substituting $\alpha = 0^\circ$and $\beta = 180^\circ$, so that,  \begin{displaymath}\vec B = \mu_0 nI\hat k\end{displaymath}

The field is very nearly constant. For points on the axis far removed from the ends but outside the solenoid, $\alpha\approx\beta$so that the field is nearly zero.

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