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. Determine the magnitudes of induced emf and current during this time-interval.

Explanation

The angle `theta` made by the area vector of the coil with the magnetic field is `45^(@)`. From Eq. (6.1), the initial magnetic flux is
`phi=BA costheta`
`=(0.1xx10^(-2))/sqrt2Wb`
Final flux, `phi_(min)=0`
The change in flux is brought about in 0.70 s. From Eq. (6.3), the magnitude of the induced emf is given by
`epsi=(abs(Deltaphi_(B)))/(Deltat)=(abs((phi-0)))/(Deltat)=10^(-3)/(sqrt2xx0.7)=1.0 mV`
And the magnitude of the current is
`I=epsi/R=(10^(-3)V)/(0.5Omega)=2mA`
Note that the earth’s magnetic field also produces a flux through the loop. But it is a steady field (which does not change within the time span of the experiment) and hence does not induce any emf.