an electric circuit is component of the three conducting rods `MO` , `ON` and `PQ` , as shown in the figure. The resistence of the rods per unit length is `lambda` . The rod `PQ` slide, as shown in the figure, at a constant velocity `v` , keeping its tilt angle relative to `ON` and `MO` fixed at `45^(@)` . At each instance the circuit is closed. The whole system is embedded in a uniform magnetic field `B` , which is directe dperpendicularly into th epage. Compute the time-dependent induced electric current

Explanation

In time `t` , distance travelled by rod `PQ=vt`
`OP=OQ=vtcos45^(@)=(vt)/(sqrt(2))`
`PQ=2vtcos45^(@)=sqrt(2)vt=l`
Total resistance of loop
`R=lambda(OP+OQ+PQ)`
`=lambda((vt)/(sqrt(2))+(vt)/(sqrt(2))+sqrt(2vt))`
`=2sqrt(2)lambdavt`
Induced emf in rod `PQ`
`e=Bvl=sqrt(2v^(2)Bt`
Induced current
`I=(e)/(R)=sqrt(2v^(2)Bt)/(2sqrt(2)lambdavt)`
`=(Bv)/(2lamda)` (constant)
Induced current is independent of time.
Since flux is increasing, induced current will be anticlockwise or direction can be given by checking polarity of battery