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 $n$ 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) :
$(A)$ In the region $0 < r < R$, the magnetic field is non-zero.
$(B)$ In the region $R < r < 2 R$, the magnetic field is along the common axis.
$(C)$ In the region $R < r < 2 R$, the magnetic field is tangential to the circle of radius $r$, centered on the axis.
$(D)$ In the region $r > 2 R$, the magnetic field is non-zero.
IIT 2013, Diffcult
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$(A)$For $0 < r < R \Rightarrow B \neq 0$
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$(D)$ For $r > 2 R \Rightarrow B \neq 0$
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