Final answer:
The inductance of the solenoid is 9.54 * 10⁻⁴ H.
Step-by-step explanation:
The inductance of a solenoid can be calculated using the formula:
L = (μ₀ * n² * A) / l
where L is the inductance, μ₀ is the permeability of free space, n is the number of turns per unit length, A is the cross-sectional area of the solenoid, and l is the length of the solenoid.
In this case, the solenoid has a length of 43.0 cm, a diameter of 8.00 cm (radius = 4.00 cm), and 740 turns. The number of turns per unit length can be calculated as n = N / l, where N is the total number of turns and l is the length of the solenoid. The cross-sectional area of the solenoid can be calculated as A = π * r², where r is the radius of the solenoid.
Plugging in the values:
L = (4π × 10⁻⁷ T·m/A) * ((740 turns) / (43.0 cm))² * (π * (4.00 cm)²) / (43.0 cm)
Simplifying the equation gives:
L = 9.54 * 10⁻⁴ H