Discuss how a moving coil galvanometer is converted into a voltmeter of different ranges.

Helmholtz coils consist of two large flat circular coils mounted with a common axis and at distance apart equal to their common radius. Show that this arrangement produces a uniform magnetic flux density over a small space midway between the coils. Derive an equation for this flux density when the coils have the same current in the direction to produce additive effect.

A tangent galvanometer consists of a flat circular coil of $\mathrm{N}$ turns and radius $r$. The coil is placed with its plane parallel to the horizontal component of the earth's magnetic field of flux density $\mathrm{B}$. A small compass mounted at the centre of the coil is deflected through $\theta$when there is a small current $\mathrm{I}$ in the coil. Show that 

$\frac{{\mathrm{\mu }}_0\mathrm{NI}}{2\mathrm{r}}=B\mathrm{tan\theta }$