A conductor of length `l` and mass `m` can slide without any friction along the two vertical conductors connected at the top through a capacitor. A uniform magnetic field `B` is set up `_|_` to the plane of paper. The acceleration of the conductor

Options

A. (a) is constant
B. (b) increases
C. ( c) decreases
D. (d) cannot say

Answer

C

Explanation

(a) let `v` is the velocity of conductor at any time, then induced emf: `e = Blv` …….(i)
Charge on capacitor: `q = Ce = CBlv`
Current in circuit: `I = (dq)/(dt) = CBI(dv)/(dt)`
for conductor: `mg - IBl = (mdv)/(dt)`
`rarr` `mg - CB^(2)l^(2)(dv)/(dt) = (mdv)/(dt)` `rarr` `(dv)/(dt) = (mg)/(m + CB^(2)l^(2))`
This is the accleration of conductor which is constant.