The point charge moves in circle as shown in figure. The magnetic field vectors at a point P on axis of circle are and at the instants the point charge is at A and C respectively as shown in the figure.

Hence as the particles rotates in circle, only magnitude of magnetic field remains constant at the point on axis P but it's direction changes. ⇒ Alternate solution ⇒ The magnetic field at point on the axis due to charged particle moving along a circular path is given by

It can be seen that the magnitude of the magnetic field at on point on the axis remains constant. But the direction of the field keeps on changing.