Module 3 : MAGNETIC FIELD
Lecture 15 : Biot- Savarts' Law
  Example 8 : Helmholtz Coil

Two coaxial circular coils of radius $a$each carry current I each in the same sense. The centres of the coils are separated by a distance $2b$. Determine the field along the axis. The set up is called ``Helmholtz coil" when the distance $2b$between the centres of the coils equals the radius $a$of each of the loop. The field in the region between the coils of such a coil is nearly uniform.

If the distance $z$along the axis is measured from the mid points of the line joining the centres of the two coils, the field strength due to the left coil at P is

\begin{displaymath}B_1 = \frac{\mu_0 I}{2}\frac{a^2}{[a^2+ (b+z)^2]^{3/2}}\end{displaymath}

and that due to the right coil is

\begin{displaymath}B_2 = \frac{\mu_0 I}{2}\frac{a^2}{[a^2+ (b-z)^2]^{3/2}}\end{displaymath}

\includegraphics{fig3.22.eps}

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