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 (that is it increases by `10^(-3) T cm^(-1 )`as one moves in the negative x-direction), and it is decreasing in time at the rate of `10^(-3) T s^(-1)`. Determine the direction and magnitude of the induced current in the loop if its resistance is 4.50 `mOmega`.

Answer

A, B, D

Explanation

`I=(EMF)/R=-(a^(2)deltaB)/(RdeltaX)v-(a^(2)deltaB)/(Rdeltat)=22.4mA`
Method II: Take `B=-10^(-3)x+7t+B_(0)` where `B_(0)` is constant
`phi=underset(y=x)overset(x+a)intadyB, epsilon=|(ddelta)/(dt)|,i=epsilon/R`