Answer: 1.8 cm
Step-by-step explanation:
Given
Inductance of the wire, L = 2.51 μH
length of wire, x = 1.19 m
L = μN²A / z, where
N = x / 2πr. If we make r subject of formula
r = x / 2πN
Also, A = πr², if we substitute the relation for r, we have
A = π * [x / 2πN]²
A = π * x² / 4π²N²
A = x² / 4πN². We then proceed to substitute the relation of A in the primary equation.
L = μN²A / z
L = μN² / z * [x² / 4πN²]
L = μx² / z4π
If we make z subject of formula, we have
z = μx² / 4πL
z = [4*10^-7 * 1.19²] / 4π * 2.5*10^-6
z = 5.66*10^-7 / 4 * 3.142 * 2.5*10^-6
z = 5.66*10^-7 / 3.142*10^-5
z = 0.018 m
z = 1.8 cm
The tube therefore, should be 1.8 cm long