Consider a hollow pipe of infinite length and radius R. The pipe has uniform distribution of charge on its surface. The pipe is rotating with angular velocity ω about its axis. The pipe is also moving

Question

Consider a hollow pipe of infinite length and radius R. The pipe has uniform distribution of charge on its surface. The pipe is rotating with angular velocity $ω$ about its axis. The pipe is also moving with velocity v along its length. There are two points P and Q as shown in the figure. Point P is inside the pipe and point Q is outside the pipe. Then match the component of magnetic field in list-I with description given in list-II.

List - I	List - II
(P) $B_{x}$ at point P	(1) is zero
(Q) $B_{x}$ at point Q	(2) depends on $ω$
(R) $B_{y}$ at point P	(3) depends on $v$
(S) $B_{z}$ at point Q	(4) inversely proportional to distance from the axis of pipe
	(5) None of these

TestHub · Accepted Answer

The rotating charged pipe is equivalent to a solenoid: inside, the field is axial (along $y$ ), proportional to $ω$ ; outside, it is zero.

The translation with speed $v$ is equivalent to an axial current $i \propto v$ : at an outside point $B = \frac{μ _{0} i}{2 π r}$ , along $z$ and inversely proportional to the distance.

Hence $B_{x}$ at P $= 0$ ; $B_{x}$ at Q $= 0$ ; $B_{y}$ at P depends on $ω$ ; $B_{z}$ at Q depends on $v$ and varies inversely with distance.

P $\to$ 1; Q $\to$ 1; R $\to$ 2; S $\to$ 3, 4

Physics - Magnetism Question with Solution | TestHub

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JEE Main 2027 (Class 12+)