Your little sister is building a radio from scratch Plans ca

Your little sister is building a radio from scratch. Plans call for a 450 H inductor wound on a cardboard tube. She brings you the tube from a toilet-paper roll (12 cm long, 4.0 cm diameter), and asks how many turns she should wind on the full length of the tube. Your answer?

Solution

mu₀ = 4 pi * 10-7 , Area = pi * r² = pi * 0.02² ,

l = 0.12 m

Inductance of a solenoid, air L = mu₀ N² A / l

450 * 10^-6 = (4 pi * 10^-7 * N² * ( pi * 0.02²) / 0.12  

N² = 34195.899

N = 184.9 = 185 turns