A square loop of side 12 cm with its sides parallel to X and Y axes is moved with a velocity of 8 cm. `s^(-1)` in the positive x-direction in an environment containing a magnetic field in the positive z-direction. The field is neither uniform in space nor constant in time. It has a gradient of `10^(-3)T.cm^(-1)` along the negative x-direction and is decreasing in time at the rate of `10^(-3)T.s^(-1)`. Determine the direction and magnitude of induced current in the loop if its resistance is 4.50 m `Omega`.

Explanation

Rate of change of B due to variation with time
`=A.(dB)/(dt)=(12xx10^(-2))^(2)xx10^(-3)`
`=1.44xx10^(-5)Wb.s^(-1)`
Rate of change of B due to variation with space
`=A.(dB)/(dx).(dx)/(dt)=(12xx10^(-2))^(2)xx10^(-3)xx8xx10^(-2)`
`=11.52xx10^(-5)Wb.s^(-1)`
Total rate of change of flux
`=(1.44+11.52)xx10^(-5)Wb.s^(-1)`
`=12.96xx10^(-5)Wb.s^(-1)`
`therefore e=12.96xx10^(-5)V`
`therefore I=(e)/(R)=(12.96xx10^(-5))/(4.5xx10^(-3))=2.88xx10^(-2)A`