A square loop of side 10 cm and resistance `0.5Omega` is placed vertically in the east-west plane. A uniform magnetic field of 0.10T 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 square loop will have its area vector (normal to the plane) perpendicular to the east-west plane. So, its angle with the magnetic field in the north-east direction is `theta=45^(@)`.
Initial flux through the coil,
`phi_(1)= B_(1)A costheta`
Here, `B_(1) = 0.10 T`, `A=10 cm xx 10 cm = 100 cm^(2) = 10^(-2) m^(2)`
`:. phi_(1) = 0.10 xx 10^(-2) xx cos 45^(@)`
`=0.10 xx 10^(-2) xx (1)/(sqrt2)=(10^(-3))/(sqrt2) Wb`
Final flux through the coil,
`phi_(2) =B_(2)A costheta`
Here, `B_(2)= 0`
`:. phi_(2)=0`
Time taken for flux change, `Deltat = 0.7 s`
Emf induced across the loop is
`|epsilon|=(dphi)/(dt)=(|phi_(1)-phi_(2)|)/(dt)=(1)/(0.7)((10^(-3))/(sqrt2))=(10^(-3))/(sqrt2 xx 0.7)`
`=10^(-3) V=1 mV`
The induced current through the coil will be `I=(|epsilon|)/(R)`
Here, `R=0.5 Omega`
`I=(1 mV)/(0.5 Omega)=2mA`