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)`.

Explanation

Rotating emf will be induced
due to rotation of the rod.
emf of part `OA` is
`epsilon_(1) = (1)/(2)BL^(2)omega`
emf of part `OC` is `epsilon = (9)/(2)BL^(2)omega`
The circuit can be separated as


`V_(A) + epsilon_(1) - epsilon_(2) = V_(c)`
`V_(A) - V_(c) = epsilon_(2) - epsilon_(1) = (9)/(2)Bl^(2)omega - (1)/(2)Bl^(2)omega = 4 Bl^(2)omega`
`V_(A) - V_(C) = 4 Bomega l^(2)`