A circular coil of wire consisting of $100$ turns, each of radius $8.0\; cm$ carries a current of $0.40\, A$. What is the magnitude of the magnetic field $B$ at the centre of the coil?
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Number of turns on the circular coil, $n=100$

Radius of each turn, $r=8.0 \,cm =0.08 \,m$

Current flowing in the coil, $I=0.4\, A$

Magnitude of the magnetic field at the centre of the coil is given by the relation

$|B|=\frac{\mu_{0}}{4 \pi} \frac{2 \pi n I}{r}$

$\mu_{0}=$ Permeability of free space $=4 \pi \times 10^{-7} \,T\,m\, A ^{-1}$

$|B|=\frac{4 \pi \times 10^{-7}}{4 \pi} \times \frac{2 \pi \times 100 \times 0.4}{0.08}$

$=3.14 \times 10^{-4}\, T$

Hence, the magnitude of the magnetic field is $3.14 \times 10^{-4}\; T$

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