Tia needs to produce a solenoid that has an inductance of 3.01 μ H 3.01 μH . She constructs the solenoid by uniformly winding 1.13 m 1.13 m of thin wire around a tube. How long, in centimeters, should the tube be?

13 cm

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