For a long cylindrical wire carrying a uniform current, the magnetic field at a distance \( r \) from the axis of the wire increases linearly with \( r \) inside the wire (for \( r < R \)), as given by Ampère's Law. Outside the wire (for \( r > R \)), the magnetic field decreases with \( 1/r \).
Therefore, the correct graph showing the variation of magnetic field \( B \) with distance \( r \) is option (A).