A square loop of side 12 cm with its sides parallel to X and Y axes is moved with a velocity of `8cms^(-1)` in the possitive 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)Tcm^(-1)` along the negative x-direction (that is it increases by `10^(-3)T` as one moves in the negative x-direction), and it is decreasing in time at the rate of `10^(-3)Ts^(-1)`. Determine the direction and magnitude of the induced current in the loop of its resistance is `4.50mOmega`.

Explanation

Rate of change of flux due to time variation in `B=144xx10^(-4)m^(2)xx10^(-3)Ts^(-1)`
`=1.44xx10^(-5)Wb//s`
Rate of change of flux due to motion of the loop in nonuniform
`B=144xx10^(-4)m^(2)xx10^(-3)Tcm^(-1)xx8cm//s=11.52xx10^(-5)Wb//s`
Net change in flux = `varepsilon=(1.44+11.52)xx10^(-5)=12.96xx10^(-5)V`
Current `I=(12.96xx10^(-5))/(4.5xx10^(-3))=2.88xx10^(-2)A`
Direction of induced current is such that it increases the magnetic flux linked with the loop in the positive direction.