A long, ideal solenoid of radius \(R\) has \(n\) turns per unit length and carries a time-dependent current given by \(I(t) = I_0 \left(1 - \dfrac{t^2}{T^2}\right)\) for \(0 \le t \le T\), where \(I_0\) and \(T\) are positive constants. Which of the following expressions gives the magnitude of the induced electric field \(E(r, t)\) at a radial distance \(r > R\) from the central axis of the solenoid as a function of time \(t\)?