A square loop of side `12 cm` with its sides parallel to `x` and `y`- axes is moved with a velocity `8 cm//s` along positive `x`-direction in an environment containing magnetic field along `+ve` z-direction. The field has a gradient of `10^(-3) "tesla"//"em"` along `-ve` x-direction (increasing along `-ve` x-axis) and also decreases with time at the rate of `10^(-3) "tesla"//s`. The emf induced in the loop is

Explanation

The magnetic field in loop varies position `'x'` of loop and also with time simultaneously.
The rate of change of flux due to variation of `'B'` with time is `(d phi)/( dt) = A xx (dB)/(dt)`
The rate of change of flux due to variation `B` with position `'x'` is
`(d phi)/(dt)=Axx(dB)/(dt) = A(dB)/(dx) xx (d x)/(dt) = A(dB)/(dx) xx v`
Since both cause decrease in flux, the two effects will add up
`:.` The net emf induced
`e = (d phi)/(dt) = A(dB)/(dt) + A(dB)/(dx) xx v = A[(dB)/(dt)+v.(dB)/(dx)]`
`= 144 xx 10^(-4)[10^(-3)+8xx10^(-3)]`
`= 144 xx 9 xx 10^(-7) = 129.6 xx 10^(-6)V`