A coil formed by wrapping 50 truns of wire in the shape of square is positioned in a magnetic field so that the normal to plane of the coil makes an angle of `60^(@)` , with the direction of the field. When the magnetic field is increased uniformly from `200muT` to `600muT` in `0.4sec` , an emf of magnitude `I00mV` is induced in the coil. What is the total length of the wire ?

Explanation

`N=50` , `theta=60^(@)` , `bar(e)=100xx10^(-3)V`
`(DeltaB)/(Deltat)=((600-200)xx10^(-6))/(0.4)=10^(-3)T//sec`
Let side of square be a
`phi=NBAcostheta=Nba^(2)cos60^(@)=(1)/(2)Nba^(2)`
`bar(e)=(Deltaphi)/(Deltat)=(1)/(2)Na^(2)(DeltaB)/(Deltat)=(1)/(2)xx50xxa^(2)xx10^(-3)`
`100xx10^(-3)=25xx10^(-3)a^(2)` implies `a=2m`
Total length of wire `=N(4a)=50xx4xx2=400m`