A conducting rod `AC` of length `4l` is rotated about point `O` in a uniform magnetic field `vec(B)` directed into the plane of the paper. `AO = l and OC = 3l`. Find `V_(A) - V_(C)`.

Options

A. `V_(A)-V_(O)=(Bomegal^(2))/(2)`
B. `V_(O)-V_(C)=(7)/(2)B omegal^(2)`
C. `V_(A)-V_(C)=4Bomegal^(2)`
D. `V_(C)-V_(O)=(9)/(2)Bomegal^(2)`

Answer

C

Explanation

For rotating rod, induced emf, `v=(1)/(2)Bl^(2)omega`

`"For part AO, "V_(OA)=V_(O)-V_(A)=(1)/(2)Bl^(2)omega`
`"For part OC, "V_(OC)=V_(O)-V_(C)=(1)/(2)B(wl)^(2)omega`
`therefore" "V_(A)-V_(C)=4Bl^(2)omega`