Final answer:
The cross-sectional area of a solenoid can be calculated using the formula for inductance after rearranging it to solve for the area. Given the inductance, number of turns, and length, the permeability of free space is also factored into the calculation.
Step-by-step explanation:
The question asks us to determine the cross-sectional area of a solenoid given its inductance, the number of turns, and its length. To solve this problem, we can rearrange the formula for the inductance of a solenoid, which is L = (N²·μ·A)/l, where L is the inductance, N is the number of turns, μ is the permeability of free space (μ = 4π x 10^-7 H/m), A is the cross-sectional area, and l is the length of the solenoid.
Given:
L = 7.1 mH (7.1 x 10^-3 H),
N = 450 turns,
l = 26 cm (0.26 m),
μ = 4π x 10^-7 H/m.
Rearrange the formula to solve for A:
A = (L·l)/(N²·μ).
Now, plug in the given values and calculate A:
A = (7.1 x 10^-3 H · 0.26 m) / (450² · 4π x 10^-7 H/m)
After computing the above expression, you will get the cross-sectional area of the solenoid.