A wire ab of length l, mass m and resistance R slided on a smooth, thick pair of metallic rails joined at the bottom as shown in . The plane of the the rails makes an angle `theta` with the horizontal. A vertical magnetic field B exists in the ragion. if the wire slides on the rails at a constant speed v, show that `B = sqrt(mg R sin theta)/(vl^2 cos^theta)`.
(##HCV_VOL2_C38_E01_076_Q01##)

Options

A. (a) `(mg)/(R )(sin theta)/(B^(2)l^(2)cos^(2)theta)`
B. (b) `(mg)/(R )(sin^(2) theta)/(B^(2)l^(2)cos^(2)theta)`
C. ( c) `(mgR sin theta)/(B^(2)l^(2)cos^(2)theta)`
D. ( d) `mgR (sin^(2) theta)/(B^(2)l^(2)costheta)`

Answer

C

Explanation

( c) `Blv cos theta = mg sin theta`
Here induced emf across slider is `(Bcos theta)lv`
`:.` Induced current `I = (Blv cos theta)/(R )`

From equation (i)
` Blcos theta(Blvcostheta)/(R ) = mg sin theta`
`:.` `v = (mg R sin theta)/(B^(2)l^(2)cos^(2) theta)`