A solenoid is designed to produce a magnetic field of 3.50×10^−2 T at its center. It has a radius of 1.80 cm and a length of 46.0 cm , and the wire can carry a maximum current of 13.0 A. Required:
a. What minimum number of turns per unit length must the solenoid have?
b. What total length of wire is required?

a. 2143 turns/m

b. 111.5 m

Explanation:

a. The minimum number of turns per unit length (N/L) can be found using the following equation:

Hence, the minimum number of turns per unit length is 2143 turns/m.

b. The total length of wire is the following:

Since each turn has length 2πr of wire, the total length is:

Therefore, the total length of wire required is 111.5 m.

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