Final answer:
To induce an emf of 2.0 V in a 10-turn solenoid with an inductance of 4.0 mH, the current must change at a rate of 500 A/s.
Step-by-step explanation:
The question asks for the rate of change of current needed in a 10-turn ideal solenoid to generate an emf of 2.0 V, given that the solenoid has an inductance of 4.0 mH. To determine this, Faraday's law of induction and the formula for an induced emf in a solenoid, which is E = -L * (dI/dt), can be used. Here, E is the induced emf, L is the inductance, and dI/dt is the rate of change of current. Rearranging the formula to solve for dI/dt, we have dI/dt = E/L. Substituting the given values: dI/dt = 2.0 V / 4.0 mH, which equals 500 A/s. So, the current should change at a rate of 500 A/s to generate an emf of 2.0 V in the solenoid.