The related concept to solve this exercise is given in the expressions that the magnetic field has both as a function of the number of loops, current and length, as well as inductance and permeability. The first expression could be given as,
The magnetic field H is given as,
Here,
n = Number of turns of the coil
I = Current that flows in the coil
l = Length of the coil
From the above equation, the number of turns of the coil is,
The magnetic field is again given by,
Where the minimum inductance produced by the solenoid coil is B.
We have to obtain n, that
Replacing with our values we have that,
Therefore the number of turn required is 28Truns