Question

A solenoid 1.39 m long and 3.20 cm in diameter carries a current of 17.1 A. The magnetic field inside the solenoid is 26.9 mT. Find the length of the wire forming the solenoid.

Answer 1

Step-by-step explanation:

It is given that,

Length of the solenoid, l = 1.39 m

Diameter of the solenoid, d = 3.2 cm = 0.032 m

Radius of solenoid, r = 0.016 m

Magnetic field inside the solenoid,
`B=26.9\ mT=26.9* 10^(-3)\ T`

We need to find the length of the wire forming the solenoid. The magnetic field inside the solenoid is given by :

`B=\mu_o nI`

n is number of turns per unit length

`B=(\mu_o NI)/(l)`

`N=(Bl)/(\mu_o I)`

`N=(26.9* 10^(-3)* 1.39)/(4\pi * 10^(-7)* 17.1)`

N = 1740.04

The total length having N loop is,

`L=2\pi r* N`

`L=2\pi * 0.016* * 1740.04`

L = 174.92 m

So, the length of the wire forming the solenoid is 174.92 meters. Hence, this is the required solution.