Final answer:
The number of turns N in a solenoid can be calculated using N = L / (πD), where L is wire length and D is the tube diameter. The length of the solenoid with a single layer of wire turns is given by L₂ = N * d. The magnetic field B inside the solenoid is determined by the formula B = μ₀ * (N/L₂) * I.
Step-by-step explanation:
To determine the characteristics of a solenoid such as the number of turns and the magnetic field, we can use some standard equations and the given parameters:
- L (length of wire) = 35 m
- D (diameter of hollow tube) = 1.5 cm
- d (diameter of wire) = 0.95 mm
- I (current) = 9.5 A
(a) The expression for the number of turns, N, in the solenoid would be N = L / (πD). This comes from the fact that each turn is the length of the circumference of the tube, and we ignore the thickness of the wire for this calculation.
(b) To calculate the number of turns, N, for the solenoid, using the given data:
N = 35000 cm / (π * 1.5 cm) ≈ 7434 turns
(c) The expression for the length of the solenoid (L₂) in terms of D, L, and d would be L₂ = N * d, assuming a single layer of turns.
(d) Calculating L₂ in meters:
L₂ = 7434 * 0.095 cm ≈ 706.23 cm ≈ 7.06 meters
(e) The magnitude of the magnetic field at the center of the solenoid in tesla can be found using the formula B = μ₀ * (N/L₂) * I, where μ₀ is the permeability of free space (4π x 10⁻⁷ T⋅m/A).