Two similar coaxial coils, separated by some distance, carry the same current I but in opposite directions. The magnitude of the magnetic field B at a point on the axis at the mid-point of the line joining the centre is :

Magnetic field at the axial point due to a current carrying loop is given as,

$\mathrm{B}=\frac{{\mathrm{\mu }}_0{\mathrm{iR}}^2}{2{\left({\mathrm{R}}^2+{\mathrm{x}}^2\right)}^{3/2}}$

As the distance of the point from the centre of the loops are same, i.e, values of x are same for the loops, magnitude of the magnetic field B will be same.

Since, the direction of the current is opposite, the direction of the magnetic field will also be opposite.

Hence, net magnetic field at the mid-point of the centre of the loops will be zero.