Chapter 28, Problem 73GP

(a)

To determine

Show that the magnetic field at position $x$ along the $x$ axis is given by, $B(x)=\frac{4{\mu }_{0}NI}{R}\left\{{\left[4+{\left(1-\frac{2x}{R}\right)}^2\right]}^{-\frac{3}{2}}-{\left[4+{\left(1+\frac{2x}{R}\right)}^2\right]}^{-\frac{3}{2}}\right\}$.

(b)

To determine

Show that the magnetic field is given by $B\approx Cx$ where the constant $C=48{\mu }_{0}NI/25\sqrt{5}{R}^2$ for small excursions from the origin where $x\ll R$.

(c)

To determine

The value of the current that should flow through the coils.