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 `2 R`. The solenoid has a `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)

Options

A. In the region `0 lt r lt R`, the magnetic field is non - zero.
B. In the region `R lt r lt 2R`. The magnetic field is along the common axis.
C. In the region `R lt r lt 2R`, the magnetic field is tangential to the circle of radius r, centred on the axis.
D. In the region `r gt 2R`, the magnetic field is non - zero.

Answer

a, d

Explanation

Magnetic field due to solenoid at points inside it is uniform and along its axis. Whereas magnetic field due to hollow cylinder is zero for points in the region ` 0 lt r lt R` and its magnetic field extends outside it in the region ` r gt R`.
Magnetic field in the region ` 0 lt r lt R` is due to solenoid, hence option (a) is correct.
Magnetic field due to solenoid is along its axis whereas magnetic field lines are circles around the hollow cylinders perpendicular to its length for points outside its surface. So we can understand that options (b) and (c) are wrong. Option (d) is also correct because magnetic field in the region `r gt 2R` is due to hollow eylinder, although magnetic field in this region due to solenoid is zero.