A square metal wire loop of side 20 cm and resistance `2Omega` is moved with a constant velcoity `v_(0)` in a uniform magnetic field of induction B = 1 `Wb//m^(2)` as shown in the figure. The magnetic field lines are perpendicular to the plane of the loop. The loop is connected to a network of resistance each of value `5Omega`. The resistances of the lead wires BF and AE are negligible. What should be the speed of the loop, so as to have a steady current of 2 mA in the loop? Give the direction of current in the loop.

Explanation

From the figure, we see that, network CEOF is balanced Wheatstone bridge, so no current will flow in branch CD.
So, the equivalent resistance of CEOF network is
`R_(eq)=(10xx10)/(10+10)=5Omega`
Resistance of loop `=2Omega`
`R_("total")=2+R_(eq)=2+5=7Omega`
We know that induced emf, `e=Bv_(0)l`
and induced current, `I=(e)/(R_("total"))=(Bv_(0)l)/(7)rArr2xx10^(-3)=(1xxv_(0)xx0.2)/(7)`
`rArr" "v_(0)=7xx10^(-2)m//s=7cm//s`
As, flux is decreasing, so induced current I will be clockwise.