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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)

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In the region $0 < r < R$ , the magnetic field is non – zero

In the region $R < r < 2 R$ , the magnetic field is along the common axis.

In the region $R < r < 2 R$ , the magnetic field is tangential to the circle of radius , centred on the axis.

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

answer is A, D.

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Detailed Solution

Assuming BC for cylinder and B_S for solenoid

$(A) R > r > 0$

$B_{S} = μ_{0} ni > O (Correct)$

$(B) 2 R > r > R$

$B = \sqrt{B_{S}^{2} + B_{C}^{2}}$ not along the axis of cylinder, hence, wrong.

$(D) r > 2 R, B = B_{C}$

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