a circular coil, of radius R, carries a current I. write the exxpression for the magnetic field due to this coil at its center. find out the direction of the magnetic field.

The expression for magnetic field due to the current at the centre of the coil is given by,
$B=\frac{{\mu }_{0}NI}{2R}$
where N is the number of turns all other has the usual meaning.
This magnetic field is perpendicular to the plane of the coil. If the current is clockwise the magnetic field is pointed inward to the plane, if the current is counter clockwise it is pointed out of the plane.