A42-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.030-t magnetic field at its center. part a if the maximum current is 4.3 a , how many turns must the solenoid have?

The magnetic field at the center of a solenoid (in vacuum) is given by

where
is the magnetic permittivity in vacuum
is the number of turns
is the length of the solenoid
is the current.

Re-arranging the formula and using , we find the number of turns N:

26.4 is about the right time