Tia needs to produce a solenoid that has an inductance of 2.51 μ H. She constructs the solenoid by uniformly winding 1.19 m of thin wire around a tube. How long, in centimeters, should the tube be?

Answer: 1.8 cm

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