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 about its axis with angular velocity $\omega$. The pipe is also translating 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. Choose the correct option(s).

• A. $B_X$ at point P is zero.
  
• B. $B_X$ at point Q depends on $\omega$.
• C. $B_Y$ at point P depends on v.
• D. $B_Z$ at point Q is inversely proportional to distance from the axis of pipe.
  
  

Answer 1

Answer: (A), (D)

$B_Z$ at point Q is inversely proportional to distance from the axis of pipe.





For a point inside pipe, pipe will act as solenoid.
Hence $\overrightarrow{B}$ will be acting along the axis.

For a point outside pipe, it will act as infinite long wire.
Hence $B_y=\frac{{\mu }_0}{2\pi }\frac{i}{r},$ here $i=e\lambda \theta$
c) $B_y$ is independent of $v,$ as $v$ is in $y$ direction.