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$\left(s\right)$ is (are) :

• A. in the region $0<r<R$, the magnetic field is non-zero
• B. in the region $R<r<2R$, the magnetic field is along the common axis
• C. in the region $R<r<2R$, the magnetic field is tangential to the circle of radius $r$, centered on the axis
• D. in the region $r>2R$, the magnetic field is non-zero

Answer 1

Answer: (A), (D)

The correct options are
A in the region $0<r<R$, the magnetic field is non-zero
D in the region $r>2R$, the magnetic field is non-zero

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.

From $r:R-\infty$ the magnetic field will be of sum of solenoid and conductor since magnetic field due to the current carrying wire is non-zero as there is current in region, and direction of field will be non axial.
$r>2R$ due to conductor and solenoid.