A rectangular loop of area vector A =[ i + 3 j ] 10^ -2 ~m ^ 2 is placed in a magnetic…

A rectangular loop of area vector \(\overrightarrow{{A}}=[\hat{i}+\sqrt{3} \hat{j}] \times 10^{-2} {~m}^{2}\) is placed in a magnetic field \(\overrightarrow{{B}}=\left[4 .0 {t}^{2}+2 .0\right] \hat{{i}}\) , where B is in tesla and t in seconds. At \({t}=1 .0 {~s}\) , the magnitude of induced emf in the loop is: