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 `theta 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 tangent to the circle of radis r, centred on the axis
D. In the region `r gt 2R`, the magnetic field is non-zero.

Answer

A, D

Explanation

Let `B_C` and `B_S` be the magnetic field due to current in cylinder C and solenoid S respectively at point P, distance r from the common axis.

(a) For `theta lt r lt R`,
`B=B_S=mu_0nI!=0` hence correct.
(b) For `R lt r lt 2R`
`B=sqrt(B_S^2+B_C^2)`
It is not acting along the axis of cylinder, hence wrong.
(c) For `R lt r lt 2R`, B is not in the plane of circle, hence wrong.
(d) For `r gt 2R, B!=0`, hence correct.