Final answer:
The inductance of a solenoid is found using the formula involving the number of turns, the cross-sectional area, the length of the solenoid, and the permeability of free space. By converting all given measurements to standard SI units and substituting into the formula, the inductance of the given solenoid is calculated to be approximately 0.043 H.
Step-by-step explanation:
The inductance of a solenoid can be calculated using the formula L = (u0 × N2 × A) / l, where u0 is the permeability of free space, N is the number of turns, A is the cross-sectional area, and l is the length of the solenoid.
Given a solenoid with 480 turns, a radius of 1.90 cm (which gives us a cross-sectional area A = π × r2), and a length of 25 cm, we can use these values to calculate the inductance. The permeability of free space, u0, is a constant equal to 4π × 10-7 H/m. Converting the radius to meters and plugging all the values into the formula gives us the inductance L.First, convert radius and length from centimeters to meters: radius = 0.019 m, length = 0.25 m. The cross-sectional area A is π × (0.019 m)2. Then, calculate the inductance using the formula: L = (4π × 10-7 H/m × 4802 × (π × 0.019 m2)) / 0.25 m.After calculating, we find that the inductance of the solenoid is approximately 0.043 H (Henrys).