A conducting circular loop is placed in X–Y plane in presence of magnetic field \( \vec{B} = (3 t^3 \, \hat{j} + 3 t^2 \, \hat{k}) \) in SI unit. If the radius of the loop is \( 1 \, \text{m} \), the induced emf in the loop, at time \( t = 2 \, \text{s} \) is \( n\pi \, \text{V} \). The value of \( n \) is _____.
