The correct answer is option 4: perpendicular to the plane containing the conductor and the point.

When a current flows through an infinitely long wire, it creates a magnetic field around it. The direction of this magnetic field can be determined using the right-hand thumb rule.

According to the right-hand thumb rule, if you imagine holding the wire in your right hand with your thumb pointing in the direction of the current, then the direction in which your curled fingers point will give you the direction of the magnetic field.

In the case of an infinitely long wire, the magnetic field lines form concentric circles around the wire. The magnetic field lines are always perpendicular to a plane containing the wire and the point where the magnetic field is being measured. This means that option 4 is the correct answer.

Options 1 and 2 are incorrect because they assume that the magnetic field is parallel or anti-parallel to the current, which is not the case for an infinitely long wire.

Option 3 is also incorrect because it assumes that the magnetic field is along the perpendicular drawn from a point on the wire, which is not true for an infinitely long wire.

Therefore, the correct answer is option 4: perpendicular to the plane containing the conductor and the point.