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jek_recluse [69]
3 years ago
15

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?
Physics
1 answer:
Anna11 [10]3 years ago
4 0

Answer:

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:

B = \frac{\mu_{0}NI}{L}

\frac{N}{L} = \frac{B}{\mu_{0}I} = \frac{3.50 \cdot 10^{-2} T}{4\pi \cdot 10^{-7} Tm/A*13.0 A} = 2143 turns/m

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

b. The total length of wire is the following:

N = 2143 turns/m*L = 2143 turns/m*46.0 \cdot 10^{-2} m = 986 turns

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

L_{T} = N*2\pi r = 986 turn*2*\pi*1.80 \cdot 10^{-2} m = 111.5 m

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

I hope it helps you!

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