Physics - Magnetism Question with Solution | TestHub

The magnetic field at the centre of a circular coil of $n$ turns is given by:

$B=\frac{{\mu }_{0}nI}{2r}$

Rearranging the formula to solve for $n$:

$n=\frac{B\times 2r}{{\mu }_{0}I}$

Substituting the given values ($B=3.14\times 10^{-4}\text{ T}$, $r=0.08\text{ m}$, ${\mu }_0=12.56\times 10^{-7}\text{ SI unit}$, $I=0.4\text{ A}$):

$n=\frac{3.14\times 10^{-4}\times 2\times 0.08}{12.56\times 10^{-7}\times 0.4}$

$n=\frac{3.14\times 10^{-4}\times 0.16}{4\times 3.14\times 10^{-7}\times 0.4}$

$n=\frac{0.16\times 10^{-4}}{1.6\times 10^{-7}}$

$n=0.1\times 10^3$

$n=100$

Answer: $100$