The current in a solenoid is 1.2 a. how many turns must be wound on a 0.25 m solenoid in order to produce a magnetic field of 1 mt within it?

N = 166 turns

Explanation:

Conceptual Analysis

The magnetic field inside a solenoid is calculated by means of the following formula:

B = μ₀*(N/L) *I   Formula (1 )

Where:

B : magnetic field inside the sollenoid (T)

μ₀ : free space permeability ( T*m/A)

N : number of turns of the solenoid

L : solenoid length (m)

I : electric current in the solenoid (A)

Known data

I= 1.2 A

L= 0.25 m

B= 1 mT = 1 *10⁻³T

μ₀ = 4π*10⁻⁷ T*m/A

Problem development

We replace data in formula (1) to calculate the number of turns of the solenoid (N):

B = μ₀*(N/L) *I

1 *10⁻³ = 4π*10⁻⁷*(N/0.25) *1.2

1 *10⁻³*0.25 =4π*10⁻⁷*1.2*N

N= (0.25*10⁻³) /(4π*10⁻⁷*1.2)

N= 165.78

N = 166 turns