Question

Tia needs to produce a solenoid that has an inductance of 2.07 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

Answer:

$l=0.068 m$

Explanation:

given,

inductance of solenoid = 2.07 μ H

winding of the wire = 1.19 m

Using formula of inductance

$L = \dfrac{\mu_0N^2A}{l}$

L is the inductance

N is number of turns of the coil

μ₀ is permeability of free space

L is length of winding

N (2π r) = 1.19          

squaring both side

4π(N²(πr²))=1.19²    

N² A = 0.113            

now                              

$2.07 \times 10^{-6}= \dfrac{4\pi\times 10^{-7}\times 0.113}{l}$

$l= \dfrac{4\pi\times 10^{-7}\times 0.113}{2.07 \times 10^{-6}}$

$l=0.068 m$