Question

A cylindrical shell of length L and radius R is uniformly charged with charge Q. This shell is rotating at angular velocity $\omega$ about its axis. If L>>R, magnetic field inside shell is

• A. $\frac{{\mu }_{0}Q\omega R}{2L^2}$
• B. $\frac{{\mu }_{0}Q{\omega }^2}{2\pi R}$
• C. $\frac{{\mu }_0\omega Q}{2\pi L}$
• D. $\frac{{\mu }_{0}Q\omega }{\pi RL}$

Answer 1

The correct option is C $\frac{{\mu }_0\omega Q}{2\pi L}$


This will behave as solenoid and field outside will be zero.
Using Ampere's law, B.$l$ = ${\mu }_0{I}_{in}$

$I_{in}=\frac{\Delta Q}{\Delta t}=\frac{Q}{L}\frac{l}{\frac{2\pi }{\omega }}=\frac{Ql\omega }{2\pi L}$

$Bl=\frac{{\mu }_{0}Ql\omega }{2\pi L}\Rightarrow B=\frac{{\mu }_{0}Q\omega }{2\pi L}$