A square loop of side `10 cm` and resistance `0.5 Omega` is placed vertically in the east-west plane. A uniform magnetic field of `0.10 T` is set up across the plane in the north-east direction. The magnetic field is decreased to zero in `0.70 s` at a steady rate. The magnitude of current in this time-interval is.

Explanation

Given, `B=0.10T`, area of squar loop `=10xx10=100cm^(2)`
`=10^(-2)m^(2)`
As the magnetic field is set up across the plane in the north-east direction, then `theta=45^(@)`
The initial magnetic flux is given by
`phi_(B)=Bscostheta`
`therefore" "phi=(0.1xx10^(-2))/(sqrt2)Wb`
`"Final flux, "phi_(min)=0" "("given")`
The change in flux is brought about in `0.70`s, i.e., `Deltat=0.70s`.
The magnitude of the induced emf is
`e=(Deltaphi_(B))/(Deltat)=(|phi-0|)/(Deltat)=(10^(-3))/(sqrt2xx0.7)~="1 mV"`
The magnitude of induced of induced current is `I=(e)/(R)=(10^(-3))/(0.5)="2 mA"`