A current I flows through a circular coil of radius R. What impact would halve the radius of the circular coil have on the magnetic field in the centre of the coil?

 The magnetic strength (dB) at location A due to current I flowing through a tiny element dl is directly proportional to the current, according to Biot Savart Law (I).

The magnetic field at the circular coil's center is given by;

$\Rightarrow \mathrm{B}=\frac{{\mu }_0\mathrm{I}}{2\mathrm{R}}$ ; Where B= strength of the magnetic field, I= current, R= radius or distance.

So, the magnetic field is inversely proportional to the radius of the coil, $\mathbf{B}\alpha \frac{1}{\mathbf{R}}$

When the radius of the coil is reduced by half, the magnetic field increases by two times.

As a result, option A is right.