(a) The magnetic field produced around a straight current carrying conductor increases on increasing the strength of current in the conductor or vice-versa.
(b) The activity described below shows that a straight conductor carrying current produces magnetic field around it.
A thick wire is inserted through the centre, normal to the plane of a rectangular cardboard. A copper wire is connected vertically between the points X and Y in series with the battery, plug and key as shown in the figure. Some iron fillings are sprinkled uniformly on the cardboard. Key is closed, so that current flows through the wire.
It is seen that, iron fillings allign themselves showing a pattern of concentric circles around the coppe wire. This represents the magnetic field lines.
Maxwell's right hand thumb rule indicates the direction of magnetic field for a known direction of current. If the thumb of the right hand points along the direction of current, then the curled fingers of that hand gives the direction of the magnetic field due to the current.
(c) The two magnetic field lines can never intersect each other because if it does so, then two tangents can be drawn at the point of their intersection, which will give two directions of the field from the same point, which is impossible.