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(s) 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: (D)

In the region r > 2R, the magnetic field is non-zero

Answer 2

In the region, 0< r < R
$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, B_P=0,$
$B_Q \ne 0,$ along the axis
\therefore\hspace15mm B_{net} \ne 0
In the region.\hspace15mm R < r < 2 R
$B_P \ne 0,$ tangential to the circle of radius r, centred on the axis.
$B_Q \ne 0,$ along the axis.
$\therefore B_{net} \ne 0,$ neither in the directions mentioned in options (b) or (c).
In region, r> 2R
\hspace15mm B_P \ne 0,
\hspace15mm B_Q \ne 0,
\therefore \hspace25mm B_{net} \ne 0,