A uniform rod of mas `m` is moving with constant velocity `v_(0)` in a perpendicular uniform magnetic field `B` as shown. The resistance of rod is `r` . The current flowing through rod, `R_(I)` and `R_(2)` will be

Options

A. `(Bv_(0)L)/(3r),(2)/(3).(Bv_(0)L)/(3r),(1)/(3).(Bv_(0)L)/(3r)`
B. `(Bv_(0)L)/(3r),(1)/(3).(Bv_(0)L)/(3r),(2)/(3).(Bv_(0)L)/(3r)`
C. `(Bv_(0)L)/(3r),(1)/(3).(Bv_(0)L)/(3r),(1)/(3).(Bv_(0)L)/(3r)`
D. `(Bv_(0)L)/(3r),(Bv_(0)L)/(3r),(Bv_(0)L)/(3r)`

Answer

B

Explanation

The rod can be replaced by a battery of emf `e=Bv_(0)l`
`i=(Bv_(0)l)/(2r+r)=(Bv_(0)l)/(3r)`
`i_(1)=(1)/(3)i=(1)/(3).(Bv_(0)l)/(3r)`
`i_(2)=i-i_(1)=(2)/(3)i=(2)/(3).(Bv_(0)l)/(3r)` .