A displacement current of 4.0 A can be set up in the space between...

The displacement current $I_d$ between the plates of a capacitor is given by the formula:

$I_d = C \dfrac{dV}{dt}$

Substituting the given values of displacement current and capacitance:

$4.0 = 6 \times 10^{-6} \times \dfrac{dV}{dt}$

$\dfrac{dV}{dt} = \dfrac{4.0}{6 \times 10^{-6}}$

$\dfrac{dV}{dt} = \dfrac{2}{3} \times 10^6 \approx 0.67 \times 10^6$ V/s

Comparing this with the given rate of change of potential difference $\alpha \times 10^6$ V/s, we get $\alpha = 0.67$.

Answer: $0.67$