Induced EMF in Primary ($V_p$): According to Faraday's law of induction, the induced electromotive force (emf) is the rate of change of magnetic flux. Given the flux linked with the primary coil is $\phi = \phi_0 + 4t$, the induced voltage in the primary is: $V_p = \left| \frac{d\phi}{dt} \right| = \frac{d}{dt}(\phi_0 + 4t) = 4 \text{ V}$

Transformer Equation: For an ideal transformer, the ratio of voltages across the primary and secondary coils is equal to the ratio of their number of turns: $\frac{V_s}{V_p} = \frac{N_s}{N_p}$ Where: $V_s$ is the secondary voltage (output). $V_p = 4 \text{ V}$ (primary voltage). $N_s = 1500$ (secondary turns). $N_p = 50$ (primary turns).

Calculation: $V_s = V_p \times \frac{N_s}{N_p}$ $V_s = 4 \times \frac{1500}{50}$ $V_s = 4 \times 30$ $V_s = 120 \text{ V}$