Answer: 13 cm
Step-by-step explanation:
Given
Inductance of the solenoid, L = 3.01•10⁻⁶ H
Width of the wire, x = 1.13 m
Length of the tube, z = ?
Now, we know that
L = μ₀N²A/z, where
N = x/2πr, making r subject of formula,
r = x/2πN
Also,
A = πr², on substituting for A, we have
A = πx²/4π²N²
Now finally, we substitute in the initial equation and solve
L = μ₀N²A/z
L = μ₀N²πx²/4π²N²z
L = μ₀x²/4z, making z subject of formula, we have
z = μ₀x²/4L
z = 4π*10⁻⁷ * 1.13² /4 * 3.01*10⁻⁶
z = (4π*10⁻⁷ * 1.2769) / (4 * 3.01*10⁻⁶)
z = 1.6*10^-6 / 1.2*10^-5
z = 0.13 m
Therefore, the length of the tube should be 13 cm