How to Calculate the Length of Wire Needed for a Solenoid?

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To calculate the total length of wire needed for a solenoid producing a magnetic field of 2.2 * 10^-2 T, the minimum number of turns per unit length is determined to be 1350 m^-1. The circumference of the solenoid, based on its radius of 1.6 cm, is essential for finding the length of one turn of wire. By multiplying the number of turns per meter by the total length of the solenoid (44 cm), the total wire length can be calculated. The dimensions provided are crucial for applying the correct equations. Understanding the relationship between turns, current, and magnetic field strength is key to solving the problem effectively.
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Homework Statement



A solenoid is designed to produce a magnetic field of 2.2 * 10^-2 t its center. It has a radius of 1.6 cm and a length of 44 cm, and the wire can carry a max current of 13 A.

The first question was what minimum number of turns per unit length must the solenoid have?

I found that to be 1350 m^-1

But the second question was what total length of wire is required?

Homework Equations



?

The Attempt at a Solution



I thought since I knew turns per unit length, current, and the magentic field that I could simply solve in reverse for this, but that's apparently not the case.

I figured that they were giving me the dimensions for something, but I'm not sure what equation to plug that into.

Any help would be greatly appreciated.
 
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Radius of the solenoid is given. The length of one tern of the wire is the circumference of the solenoid. You have calculated the number of the terns per meter. From that find the length of the wire required to construct the solenoid of the given length
 

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