A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 4.5 A, how many turns must the solenoid have?

Explanation:

The magnetic field produced is expressed using the formula

B is the magnetic field = 0.30T

I is the current produced in the coil = 4.5A

is the magnetic permittivity in vacuum = 1.26*10^-6Tm/A

L is the length of the solenoid = 32 cm = 0.32 m

N is the number of turns in the solenoid.

Making N the subject of the formula from the equation above;

Substituting the give values to get N;

The number of turns the solenoid must have is approximately 16,931 turns

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nah.   i'm just sleepy.