Two concentric circular coils of 10 turns each are situated in the same plane. Their radii are 20 cm and 40 cm and they carry 0.2 A and 0.3 A currents respectively in opposite directions. The magnetic field at the center is

$\frac{5}{4}μ_0T$

The correct answer is Option (4) → $\frac{5}{4}μ_0T$

Magnetic field due to a coil,

$B=\frac{μ_0nI}{2r}$

for coil 1,

$B_1=\frac{μ_0n_1I_1}{2r_1}=\frac{4π×10^{-7}×10×0.2}{2×0.2}$

$=2π×10^{-6}T$

for coil 2,

$B_2=\frac{μ_0n_2I_2}{2r_2}=\frac{4π×10^{-7}×10×0.3}{2×0.4}$

$=1.5π×10^{-6}T$

$∴ΔB=B_1-B_2$

$=(1.5π×10^{-6}-2π×10^{-6})T$

$≃1.57×10^{-6}Wb/m^2=\frac{5}{4}μ_0T$