A device proposed for using the voltage to measure the angular velocity ? of a shaft is shown in…
A device proposed for using the voltage 
to measure the angular velocity Ω of a shaft is shown in Fig. P5.8.3a. A cylindrical grounded electrode has radius R. (The resistance 
is “small.”) Outside and concentric at r = a is a rotating shell supporting the surface charge density distribution shown in Fig. P5.8.3b
Fig. P5.8.3a , Fig. P5.8.3b
. 
(a) Given 
and 
, show that in regions (a) and (b), respectively, outside and inside the rotating shell,
(b) Show that the charge on the segment of the inner electrode attached to the resistor is
where 
is the length in the 
direction.
(c) Given that 
, show that the output voltage is related to Ω by
