Magnetics 2 Question 18
18. 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) (2013 Adv.)
(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
Integer Answer Type Questions
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Answer:
Correct Answer: 18. (b)
Solution:
$P \rightarrow$ Hollow cylindrical conductor $Q \rightarrow$ Solenoid
In the region, $0<r<R$
$$ B _P=0, $$
$B _Q \neq 0$, along the axis
$$ \begin{array}{ll} \therefore & B _{\text {net }} \neq 0 \\ \text { In the region, } & R<r<2 R \end{array} $$
$B _P \neq 0$, tangential to the circle of radius $r$, centred on the axis. $B _Q \neq 0$, along the axis.
$\therefore B _{\text {net }} \neq 0$ neither in the directions mentioned in options (b) or (c). In region, $r>2 R$
$$ \begin{aligned} B _P & \neq 0 \\ B _Q \neq 0 & \Rightarrow B _{\text {net }} \neq 0 \end{aligned} $$
