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 `0ltr ltR` 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 centered on the axis .
D. In the region `r gt 2R` the magnetic field is n-n-zero .

Answer

`A,D`

Explanation

Assuming `B_(C)` for cylinder and `B_(5)` for solenoid
`(A) R gt r gt o`
`B_(s) = mu_(0) ni gt 0` (Correct)
`(B) 2 R gt r gt R`
`B = sqrt(B_(s)^(2)+B_(C)^(2))` not along the axis of cyliner hence wrong
` C ` Wrong not in the plane of circle
`(D) r gt 2R,B =B_(C)`
.