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