A metallic rod of length l is rotated at a constant angular speed `omega`, normal to a uniform magnetic field B. Derive an expression for the current induced in the rod, if the resistance of the rod is R.

Explanation

Let T be the time taken by the rod to complete one revolution.

Area swept by the metallic rod to rotate by an angle e in time t is
`A= (theta)/(2pi)(piL^(2))=(L^(2)theta)/(2)`
Magnetic flux linked with it is
`phi=BA cos theta`
Here, `theta=0^(@)`
`implies phi=(BL^(2)theta)/(2)`
The eml induced in the rod is given by
`|epsilon|=(dphi)/(dt)`
`=(d)/(dt)((BL^(2)theta)/(2)=(BL^(2))/(2))(d theta)/(dt)`
Here, `theta=omegat`
`:. (d theta)/(dt)=omega`
`|epsilon|=(BL^(2)omega)/(2)`
Induced current
`I=(|epsilon|)/(R)=(1)/(2).(BL^(2)omega)/(R)`