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Question:

A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is placed coaxially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries a steady current I. Consider a point P at a distance r from the common axis. The correct statement(s) is (are):
in the region 0 < r < R, the magnetic field is non-zero
in the region R < r < 2R, the magnetic field is along the common axis
in the region R < r < 2R, the magnetic field is tangential to the circle of radius r, centered on the axis
in the region r > 2R, the magnetic field is non-zero

in the region R < r < 2R, the magnetic field is along the common axis

in the region R < r < 2R, the magnetic field is tangential to the circle of radius r, centered on the axis

in the region 0 < r < R, the magnetic field is non-zero

in the region r > 2R, the magnetic field is non-zero

Solution:

From r:0-R the magnetic field will be of solenoid since magnetic field due to the current carrying wire is zero from amperes law as there is no current in region. Due to the field of solenoid, the overall magnetic field is non zero in region 0 < r < R along it's axis.