Question

A disc of radius `R` is rolling without sliding on a horizontal surface with a velocity of center of mass `v` and angular velocity `omega` in a uniform magnetic field `B` which is perpendicular to the plane of the disc as shown in Fig. 3.179. `O` is the center of the disc and `P, Q, R, and S` are the four points on the disc. Which of the following statements is true?

A. (a) Due to translation, induced emf across `PS = Bvr`
B. (b) Due to translation, induced emf across `QS = 0`
C. ( c) Due to translation, induced emf across `RO = 0`
D. (d) Due to translation, induced emf across `OQ = Bvr`

Answer 1

Correct Answer - A::B::C::D
(a,b,c,d):
Due to rotaion, `emf = (Br^(2)omega)/(2)`
Due to translation indeed emf `= Bvr`
where `r` is the separation.