b
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 \(3.14 \times 10^{-4}\; T\)