Question

How many turns should a 10-cm long ideal solenoid have if it is to generate a 1.5-mT magnetic field when 1.0 A of current runs through it? (μ0 = 4???? × 10-7 T · m/A)

Answer 1

N=119.34 turns

Step-by-step explanation:

The magnetic field of a solenoid is calculated using the formula:

B= µo*
`(I*N)/(L)` Equation 1

Where:

B: magnetic field in Teslas (T)

µo: free space permeability in T*m/A

I= Intensity of the current flowing through the conductor in ampere (A)

N= number of turns

L= solenoid length in meters (m)

Data of the problem:

L=10cm=
`10*10^(-2)`, B= 1.5mT=
`1.5*10^(-3) T` ,I=1A

µo=
`4\pi *10^(-7) (T*m)/(A)`

We cleared N of the equation (1):

N=B*L/ µo*I

N=
`(1.5*10^(-3) *10*10^(-2) )/(4\pi *10^(-7) *1`

`N=0.1193*10^(3)`

Answer

N=119.34 turns