The magnetic field line passing through the center of a circular current carrying coil is a straight line.
True
In a circular coil the field lines near the coil are circular because the field near edges is effected by only one small part of coil which is close to the point but as we move towards the center, the field is affected by all the parts of the coil equally and the sum of the effects is such that the field becomes nearly straight line as shown in the figure below.
In the vicinity of wire at P and Q, the magnetic field lines are nearly circular. Within the space enclosed inside the wire (i.e. between P and Q) magnetic field lines are in the same direction. Near the centre of the loop, the magnetic field lines are nearly parallel to each other, so the magnetic field may be assumed to be nearly uniform in a small space near the centre. At the centre, the magnetic field lines are along the axis of the loop and normal to its plane.