Final answer:
The time constant of the circuit is 0.4 seconds.
Step-by-step explanation:
The time constant of an inductor is given by the formula τ = L/R, where L is the inductance and R is the resistance. In this problem, the inductor stores 64 J of magnetic field energy and dissipates energy at the rate of 640 W when a current of 8 A is passed through it. From this information, we can calculate the inductance by using the formula Eind = 1/2 LI^2, where Eind is the energy stored in the magnetic field and I is the current.
Plugging in the given values, we get: 64 J = (1/2)L(8 A)^2. Solving for L, we find L = 2 J/A^2. The resistance can be calculated by using the formula P = IV, where P is the power dissipated, I is the current, and V is the voltage. Plugging in the given values, we get: 640 W = 8 A * V. Solving for V, we find V = 80 V. Now, we can calculate the time constant: τ = L/R = (2 J/A^2) / 80 V = 0.025 s, which is equivalent to 0.4 seconds.