A conducting wire of length `l` and mass `m` can slide without friction on two parallel rails and is connected to capacitance `C`. The whole system lies in amagnetic field `B` and a constant force `F` is applied to the rod . Then

Options

A. (a) the rod moves with constant velocity.
B. (b) the rod moves with an acceleration of `(F)//(m + B^(2)l^(2)C)`.
C. (c ) there is constant charge on the capacitor.
D. (d) charge on the capacitor increases with time.

Answer

B, D

Explanation

(b, d):
`I = (dq)/(dt) = (d)/(dt)(CvBl) = CBl(dv)/(dt) = Cbla`
`:.` `F - CB^(2)l^(2)a = ma`
`rarr` `a = (F)/(M + B^(2)l^(2)C)`
`rarr` emf increases
`rarr` charge increases.