You have two cylindrical solenoids, one inside the other, with the two cylinders concentric. The outer solenoid has length \(\ell_{\text {ourer }}=400 \mathrm{~mm}\), radius \(R_{\text {outer }}=50 \mathrm{~mm}\), and \(N_{\text {outer }}=1000\) windings. The inner solenoid has length \(\ell_{\text {inner }}=40 \mathrm{~mm}\), radius \(R_{\text {inner }}=20 \mathrm{~mm}\), and \(N_{\text {inner }}=\) 150 windings. The inner solenoid is centered within the outer solenoid. When the outer solenoid carries a current given by \(I(t)=I_{0} \sin (\omega t)\), with \(I_{0}=600 \mathrm{~mA}\) and \(\omega=\) \(100 \mathrm{~s}^{-1}\), what is the peak emf in the inner solenoid?