Question

Why sign convection of outwards is cross and inwards in dot?

Answer 1

It is just a convection

Just assume not a particular reason

By placing the thumb of the right hand in the direction of the flowing current we can find the direction of the magnetic field lines in the direction of the point of the finger. So direction of the field will be tangent to the curved lines.

In the above case, we have direction of the magnetic field coming out of the plane of the paper in the upper side of the wire. This direction is shown by a dot [ . ]

In the part below the wire direction of the magnetic field will be going in to the plane of paper. This direction is shown by a cross [ × ]

Similarly, direction of the field at any point P will be given by the tangent to the circle