How long should I take a wire with a diameter of 0.1 mm?

How long is a 0.1 mm diameter wire needed to make a single-layer solenoid with an inductance of 1 mH? The cross-sectional area of ​​the solenoid is 7.5 cm^2. The core is missing.

Solution tasks 31176:

Given: L = 1 mH - solenoid inductance S = 7.5 cm^2 - solenoid cross-sectional area d = 0.1 mm - wire diameter

You need to find: l - wire length

The formula for calculating the inductance of a single-layer solenoid without a core: L = (μ * N^2 * S) / l, where μ = 4π * 10^-7 H/m is the magnetic constant, N is the number of turns, l is the length of the wire.

Let's move l to the left side of the equation and transform: l = (μ * N^2 * S) / L

The value of the magnetic constant μ is considered known and equal to 4π * 10^-7 H/m.

The number of turns N for a single-layer solenoid without a core can be calculated by the formula: N = (l / d) + 1/2, where d is the wire diameter.

Let's move l to the left side of the equation and transform: l = (N - 1/2) * d

Substitute the expression for N into the formula for l and get the final formula for calculating the length of the wire: l = ((μ * ((l / d) + 1/2)^2 * S) / L - 1/2) * d

Let's substitute the known values ​​and solve the equation: l = ((4π * 10^-7 H/m * ((l / 0.1 mm) + 1/2)^2 * 7.5 cm^2) / 1 mH - 1 /2) * 0.1 mm l ≈ 90.5 m

Answer: The wire length should be about 90.5 m.

Calculation of wire length for a single-layer solenoid without a core

This digital product is a detailed solution to the problem of calculating the length of a 0.1 mm diameter wire to produce a single layer coreless solenoid with a given inductance of 1 mH and a cross-sectional area of ​​7.5 cm^2.

Product Features:

• Detailed description of the problem and conditions for its solution
• Using the formulas and laws necessary to calculate wire length
• Derivation of the calculation formula and answer
• Beautiful design using HTML tags

Advantages:

• It will help you quickly and accurately calculate the required wire length for the manufacture of a single-layer solenoid
• Allows you to easily understand the applied formulas and laws
• Convenient and beautiful product design

Customer reviews:

• "Great product! Quickly calculated the required wire length for my solenoid."
• "Very clear and detailed description of the task. Thank you!"
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Cost: 100 rubles

To make a single-layer coreless solenoid with an inductance of 1 mH and a cross-sectional area of ​​7.5 cm^2, it is necessary to take a wire with a diameter of 0.1 mm and a length of about 90.5 m.

To solve the problem, a formula is used to calculate the inductance of a single-layer solenoid without a core: L = (μ * N^2 * S) / l, where μ is the magnetic constant, N is the number of turns, l is the length of the wire.

The number of turns N for a single-layer solenoid without a core can be calculated by the formula: N = (l / d) + 1/2, where d is the wire diameter.

After substituting the known values ​​and solving the equation, we find that the length of the wire should be about 90.5 m.

This digital product is a detailed solution to the problem of calculating the length of a 0.1 mm diameter wire to produce a single layer coreless solenoid with a given inductance of 1 mH and a cross-sectional area of ​​7.5 cm^2.

The advantages of the product are assistance in quickly and accurately calculating the required wire length, a clear description of the task and the formulas and laws used, and a convenient and beautiful design. The cost of the product is 100 rubles.

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