A square metal wire loop of side 0.10 m and resistance `1 Omega` is moved at a constant velocity `nu_0` in a uniform magnetic field of induction `B=2 Wb m^(-2)` as shown in the figure . The magnetic field lines are `bot` to the plane of the loop directed into the paper. The loop is connected to a network of resistors each of value `3 Omega`. The resistance of lead wires OS and PQ are negligible . what should be the speed `nu_0` of the loop so as to have a steady current of 1mA in the loop ? Also indicate the direction of current in the loop .

Explanation

The equivalent resistance of the network `=3 Omega`
The resistance of the loop `=1 Omega`
`therefore` Total resistance `R=3 +1 =4 Omega`
Electro motive force in the loop `=e=Blnu_0`
Current in the loop , `i=e/R=(Blnu_0)/R`
`therefore nu_0 =(iR)/(Bl), "Here" i=1mA = 10^(-3)A`
`R = 4Omega ,B=2T , l=0.1m `
`therefore nu_0 =(10^(-3)xx4)/(2xx0.1)=2xx10^(-2) ms^(-1)`