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Gnesinka [82]
3 years ago
14

A 2.0-cm-diameter, 15-cm-long solenoid is tightly wound with one layer of wire. A 2.5 A current through the wire generates a 3.0

mT magnetic field inside the solenoid. What is the diameter of the wire, in mm?
Physics
1 answer:
sweet [91]3 years ago
5 0

Answer:

d = 1.047 mm

Explanation:

given,

diameter of the wire = 2.0-cm

length of solenoid = 15 cm = 0.15

Current in the wire = I = 2.5 A

magnetic field = B = 3.0 mT

Magnetic field inside the solenoid

        B = \dfrac{\mu_0 N I}{L}

        B = \dfrac{\mu_0 N I}{L}

               N x d = l

        N = \dfrac{l}{d}

        B = \dfrac{\mu_0 \dfrac{l}{d} I}{L}

        3 \times 10^{-3} = \dfrac{4\pi \times 10^{-7}\times \dfrac{0.15}{d}\times 2.5}{0.15}

        0.45 \times 10^{-3}\ d = 4\pi \times 10^{-7}\times 0.15\times 2.5

        \ d = \dfrac{4\pi \times 10^{-7}\times 0.15\times 2.5}{0.45 \times 10^{-3}}

               d = 1.047 x 10⁻³ m

               d = 1.047 mm

diameter of the wire is d = 1.047 mm

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